Enumerative and analytic combinatorics Thursday December 8, 2022, 2PM, Salle 3052 et zoom Amanda Burcroff (Harvard) Dyck Path Expansion Formulas for Rank 2 Cluster Algebras The theory of cluster algebras, introduced twenty years ago by Fomin and Zelevinsky, gives us a combinatorial framework for understanding the previously opaque nature of certain algebras. Each cluster algebra is generated by its cluster variables, which are defined recursively via the process of mutation. In the rank two case, several explicit formulas have been given for the cluster variables in terms of combinatorial, representation theoretic, and tropical objects. We will focus on two such formulas. The first, given by Lee-Schiffler, sums over collections of colored Dyck subpaths, and the second, given by Lee-Li-Zelevinsky, sums over compatible pairs in Dyck paths. We will discuss a correspondence between these two sets of objects, as well as a simplification and quantum generalization of the Lee-Schiffler expansion formula. Enumerative and analytic combinatorics Thursday December 1, 2022, 2PM, Salle 1007 et zoom Groupe De Lecture - Eva Philippe (Eva Philippe (IMJ-PRG)) Nu-Tamari lattice and Nu-associahedron The goal of this talk is to present the article “Geometry of the $nu$-Tamari lattices in types A and B”, by Cesar Ceballos, Arnau Padrol, Camilo Sarmiento. We will present the nu-Tamari lattice, a generalization of the Tamari lattice where the parameter $nu$ is a lattice path. One incarnation of the nu-Catalan objects is given by the lattice paths weakly above nu. We will explain briefly how certain nu-Tamari lattices partition the usual Tamari lattice. We will focus on the geometric realization of this lattice as a triangulation of a certain polytope. This relies on another incarnation of nu-Catalan objects, the (I, J)-trees introduced by Ceballos-Padrol-Sarmiento. Enumerative and analytic combinatorics Thursday November 24, 2022, 11AM, IHP Seminaire Flajolet TBD https://semflajolet.math.cnrs.fr/ Enumerative and analytic combinatorics Thursday November 17, 2022, 2PM, Salle 3052 et zoom Grant Barkley (Harvard University) Extending the weak Bruhat order The weak (Bruhat) order is a partial order on the elements of a Coxeter group W. Its Hasse diagram describes the 1-skeleton of the permutahedron. For finite Coxeter groups, the weak order has least upper bounds and greatest lower bounds, making it a lattice. But in infinite Coxeter groups, we can fail to have common upper bounds for two elements. Matthew Dyer introduced a poset called extended weak order, motivated by the geometry of the weak order, which contains the usual weak order as a subposet. It is conjectured that the extended weak order is always a lattice, even for infinite Coxeter groups. Recently with David Speyer we have proved this conjecture for the case of affine Coxeter groups. We'll discuss these ideas, focusing on the infinite symmetric group and affine symmetric group. Enumerative and analytic combinatorics Thursday November 10, 2022, 2PM, Salle 3052 et zoom Wenjie Fang, Guillaume Laplante-Anfossi Sous-posets de degré maximal des treillis $\nu$-Tamari Dans un article récent (arXiv:2208.11417), Aram Dermerjian considère les sous-posets des treillis $\nu$-Tamari constitués par les éléments de degré sortant (resp. entrant) maximal. Il s’intéresse en particulier au cas des treillis $m$-Tamari, et montre que l’un de ces sous-posets est isomorphe à un poset « $m$-Tamari glouton », généralisant l’ordre dextre défini par Frédéric Chapoton sur les chemins de Dyck. Après avoir présenté les définitions et principaux résultats de l’article, nous exposerons une conjecture de Chapoton liant les posets 1-Tamari gloutons à un sous-poset du produit du treillis de Tamari avec lui-même, défini géométriquement à partir d’une approximation cellulaire de la diagonale de l’associaèdre. Enumerative and analytic combinatorics Thursday October 27, 2022, 2PM, Salle 3052 et zoom Eva-Maria Hainzl (TU Wien) Pattern occurences in random maps In this talk, we will discuss some results and ongoing work concerning central limit theorems for pattern occurences in random planar maps. Based on a toy example ('double glued squares') we discuss our current approach and the challenges to extend it to general patterns of arbitrary size. Enumerative and analytic combinatorics Thursday October 20, 2022, 2PM, Salle 1007 et zoom Jon Boretsky (Harvard) The Nonnegative Flag Variety and its Tropicalization The flag variety of rank $r=(r_1,\dots,r_k)$ has points corresponding to collections of subspaces $(V_1,\dots, V_k)$ with $V_i$ of dimension $r_i$ such that $V_i$ is contained in $V_{i+1}$. It can be embedded into a multi-projective space, where it is cut out by the incidence Plücker relations. We explore two natural extensions of this variety: First, we study the nonnegative flag variety, which corresponds to a subset of the flag variety consisting of flags that can be represented by totally positive matrices. Second, we study the tropicalization of the flag variety and, more specifically, its nonnegative part. In both cases, we provide equivalent descriptions of these spaces for flag varieties of rank $r=(a,a+1,...,b)$, where $r$ consists of consecutive integers. In the former case, we give a condition in terms of nonnegativity of the multi-projective coordinates. In the latter, we identify the nonnegative tropical flag variety with the nonnegative flag Dressian, even though the tropical flag variety and the flag Dressian differ in general. We also explore descriptions of the nonnegative tropical flag variety in terms of polytopal subdivisions. The supports of points in the nonnegative flag Dressian give a natural notion of a flag positroid. Once again restricting to the consecutive rank case, we give a combinatorial description of flag positroids. This talk is partially based on joint work with Chris Eur and Lauren Williams. Enumerative and analytic combinatorics Thursday October 13, 2022, 12AM, Salle 3052 et zoom Jiyang “johnny” Gao (Harvard) Balanced Shifted Tableaux We introduce balanced shifted tableaux, as an analogue of balanced tableaux of Edelman and Greene, from the perspective of root systems of type B and C. We show that they are equinumerous to standard Young tableaux of the corresponding shifted shape by presenting an explicit bijection. Enumerative and analytic combinatorics Thursday October 13, 2022, 2PM, Salle 3052 et zoom Groupe De Lecture - Viviane Pons (LISN) Tamari lattice and Weak order We present the relation between the weak order / permutohedra on one hand and the Tamari lattice / associahedra on the other hand. In particular, we show how the Tamari lattice can be constructed as a sub lattice and a quotient lattice of the weak order. Finally, we present how this relates to Tamari intervals. Enumerative and analytic combinatorics Thursday October 6, 2022, 2PM, IHP Seminaire Flajolet Jehanne Dousse, Nicolas Bonichon, Thierry Levy https://semflajolet.math.cnrs.fr/ Enumerative and analytic combinatorics Thursday September 29, 2022, 2PM, Salle 3052 Houcine Ben Dali (IECL (Université de Lorraine), IRIF (Université de Paris)) Integrality in the matching-Jack conjecture Using Jack polynomials, Goulden and Jackson have introduced a one parameter deformation $τ_b$ of the generating series of bipartite maps. The Matching-Jack conjecture suggests that the coefficients $c^λ_{µ,ν}$ of the function $τ_b$ in the power-sum basis are non-negative integer polynomials in the deformation parameter $b$. Dołega and Féray have proved in 2016 the “polynomiality” part in the Matching-Jack conjecture. In this talk I present a proof for the “integrality” part. The proof is based on a recent work in which I obtain the Matching-Jack conjecture for marginal sums $c^λ_{µ,m}$ from an analog result for the $b$-conjecture, established in 2020 by Chapuy and Dołega. Jack polynomials orthogonality gives a linear system relating the coefficients $c^λ_{µ,ν}$ to the marginal coefficients $c^λ_{µ,m}$. Using a graded version of the Farahat-Higman algebra we prove that this system is invertible in $\mathbb{Z}$. Enumerative and analytic combinatorics Thursday September 22, 2022, 2PM, Salle 3052 et zoom Groupe De Lecture - Intervalles De Tamari Corentin Henriet et Matthieu Josuat-Verges Enumerative and analytic combinatorics Thursday September 15, 2022, 2PM, Salle 3052 et zoom Doriann Albertin (LIGM, Université Gustave Eiffel) The canonical complex of the weak order The canonical join complex of a join-semidistributive lattice L is a simplicial complex whose faces are in bijection with the elements of L and record the canonical join representations in L. We introduce the canonical complex of a semidistributive lattice L, another simplicial complex containing both the canonical join and meet complexes, and whose faces are in bijection with intervals of L. Like the canonical join complex, the canonical complex is flag, and behaves well with quotients of L. In 2015, N. Reading introduced the non-crossing complex, a combinatorial model for the canonical join complex of the right weak order on permutations. Its faces are described with non-crossing arc diagrams. We focus in this talk on the example of the weak order, and extend this combinatorial model to a description of the canonical complex of the weak order, the semi-crossing complex, and its faces, the semi-crossing arc bidiagrams. This allows us to compute a generalization of the Kreweras complement on non-crossing partitions to all quotients of the weak order. Enumerative and analytic combinatorics Thursday September 8, 2022, 2PM, Salle 3052 et zoom Khaydar Nurligareev (LIPN Paris Nord) Asymptotic probability of irreducible labeled objects in terms of virtual species There are various combinatorial structures that admit a notion of irreducibility in a broad sense, including connected graphs, irreducible tournaments, indecomposable permutations and different models of connected surfaces. We are interested in the probability that a random labeled object is irreducible, as its size tends to infinity. The aim of this talk is to show that, in certain cases, the asymptotics for this probability can be obtained in a common manner and the asymptotic coefficients have a combinatorial meaning naturally expressed in terms of virtual species. Moreover, we will explain how to get the asymptotic probability that a random labeled object has a given number of irreducible parts, and we will indicate the combinatorial meaning of the coefficients involved in the corresponding asymptotic expansions. This is a joint work with Thierry Monteil. Enumerative and analytic combinatorics Thursday June 30, 2022, 2PM, Salle 1007 Lucia Rossi (Graz) Limit words for $N$-continued fractions Given $N\geq 1$ and $x \in [0, 1]\backslash \mathbb{Q}$, an $N$-continued fraction expansion of $x$ is defined analogously as the classical continued fraction, but with the numerators being all equal to $N$. We introduce two infinite words $\omega(x, N )$ and $\hat\omega(x, N )$ on a two letter alphabet, which are related to the $N$-continued fraction expansion of $x$ and are obtained as a limit word of a sequence of substitutions. We call them $N$-continued fraction words. When $N=1$, we are in the classical case and find a Sturmian word. We show that these words are $C$-balanced for some explicit values of $C$, and we compute the factor complexity function of both families of words. We relate this to the more general setting of limit words of non unimodular $S$-adic sequences. This is joint work with Jörg Thuswaldner and Niels Langeveld. Enumerative and analytic combinatorics Thursday June 23, 2022, 2PM, Salle 3052 et zoom Marc Noy (UPC) Counting 3-connected bipartite maps We provide a solution to the problem of counting rooted 3-connected bipartite planar maps. Our starting point is the enumeration of bicoloured planar maps according to the number of edges and monochromatic edges (Bernardi and Bousquet-Mélou 2011). The decomposition of a map into 2- and 3-connected components allows us to obtain the generating functions of 2- and 3-connected bicoloured maps. Setting to zero the variable marking monochromatic edges we obtain the generating function of 3-connected bipartite maps, which is algebraic of degree 26, from which we deduce from an asymptotic estimate. This is joint work with Clément Requilé and Juanjo Rué. Enumerative and analytic combinatorics Thursday June 16, 2022, 2PM, Salle 3052 et zoom Sandrine Brasseur (Université Catholique de Louvain) The eight-vertex model and combinatorics We are interested in the eight-vertex (8V) model, an integrable 2D lattice model. We consider a particular sub-family of its parameters, the “supersymmetric” or “combinatorial line”, dubbed so due to its surprising links to enumerative combinatorics. Our goal, in this talk, is to provide evidence of the fascinating interplay between the 8V model and combinatorial structures, such as alternating sign matrices, plane partitions, 3-colorings,… To do so, we investigate the row-to-row transfer matrix of the model. For an odd number of columns and horizontal periodic boundary conditions, its largest eigenvalue has been shown to have a remarkably simple expression. Moreover, the associated eigenvector is a key ingredient in the computation of 8V partition functions. Ultimately, we obtain exact expressions for some components of this eigenvector and 8V partition functions in terms of symmetric polynomials introduced by Rosengren and Zinn-Justin. We then expose the links between our results and the aforementioned combinatorial structures. This talk is based on joint work with Christian Hagendorf (arXiv:2009.14077 [math-ph]). Enumerative and analytic combinatorics Thursday June 9, 2022, 2PM, Salle 3052 et zoom David Keating (University of Wisconsin) k-tilings of the Aztec diamond We will study $k$-tilings ($k$-tuples of domino tilings) of the Aztec diamond. We assign a weight to each $k$-tiling, depending on the number of ``interactions“ between the dominos of the different tilings. We will compute the generating polynomials of the $k$-tilings by showing that they can be seen as the partition function of an integrable colored vertex model. These partition functions are related to the LLT polynomials of Lascoux, Leclerc, and Thibon. We will then prove some combinatorial results about $k$-tilings in certain limits of the interaction strength. Enumerative and analytic combinatorics Thursday June 2, 2022, 11AM, IHP Seminaire Flajolet Seminaire Flajolet Enumerative and analytic combinatorics Thursday May 19, 2022, 2PM, Salle 3052 et zoom Valentin Bonzom Hiérarchie intégrable BKP et applications aux cartes non-orientées Plusieurs familles de cartes comme les triangulations et les cartes biparties comptées par taille et genre admettent des formules de récurrence remarquablement simples qui permettent de générer ces nombres efficacement. De manière intrigante, on ne sait prouver ces récurrences que par des équations issues des systèmes intégrables appelées hiérarchie KP. Dans cet exposé, j'expliquerai en termes de développement sur les fonctions de Schur ce que signifie pour une série génératrice de satisfaire la hiérarchie KP, et je donnerai plusieurs manières de la prouver dans le cas bien connu des factorisations de permutations (qui correspond également aux constellations et aux nombres de Hurwitz pondérés). Je présenterai le défi du passage aux modèles de cartes non-orientées par une tension entre développement sur les fonctions de Schur et sur les polynomes zonaux et j'évoquerai le problème connexe de la b-conjecture de Goulden et Jackson. Enfin je montrerai comment nous avons pu prouver une hiérarchie intégrable dans un cas assez résistant aux méthodes établies, celui de la série génératrice des nombres de Hurwitz monotones non-orientés. Ce sont des travaux en collaboration avec Guillaume Chapuy et Maciej Dolega. https://cnrs.zoom.us/j/94236281873?pwd=LzIyV3F5Q0JtVzN4ZU0waW84M0pVUT09 Enumerative and analytic combinatorics Friday May 13, 2022, 2:30PM, Salle 3052 et zoom Christophe Reutenauer (UQAM, Canada) Le monoïde stylique (seminaire joint Combinatoire et Automates) Le monoïde stylique Styl(A) est un quotient fini du monoïde plaxique de Lascoux et Schützenberger. Il est obtenu par l'action naturelle (insertion de Schensted à gauche) du monoïde libre A* sur l'ensemble des (tableaux) colonnes sur A. Il est en bijection avec un ensemble de tableaux semi-standards particuliers, appelés N-tableaux; la bijection consiste en une variante de l'algorithme de Schensted. On en déduit une bijection avec les partitions (ensemblistes) des sous-ensembles de A, et la cardinalté de Styl(A) est le nombre de Bell B_{n+1}, n=|A|. Une présentation de ce monoïde est obtenue en ajoutant aux relations de Knuth les relations d'idempotence a^2=a, pour chaque générateur a dans A. L'involution naturelle de A*, qui retourne les mots et renverse l'ordre de l'alphabet, induit un anti-automorphisme de Styl(A); il se calcule directement sur les N-tableaux par une variante de l'évacuation de Schützenberger. Le monoïde stylique apparaît comme le monoïde syntaxique de la fonction qui à un mot associe la longueur de son plus long sous-mot décroissant. https://u-paris.zoom.us/j/84811442271?pwd=cCtvOVc5dXZFaUErbEpyR2pNUlRCUT09 Enumerative and analytic combinatorics Thursday May 12, 2022, 2PM, Salle 3052 et zoom Baptiste Rognerud (IMJ-PRG) Les matrices de Coxeter des ensembles ordonnés de Tamari sont périodiques La matrice de Coxeter d'un ensemble ordonné fini est une matrice définie combinatoirement à l'aide de sa matrice d'incidence. Au début des années 2000, Chapoton a remarqué que les matrices de Coxeter de certains ensembles ordonnés remarquables sont périodiques. Il démontre, en utilisant la théorie des opérades, que c'est le cas des ensembles de Tamari et il conjecture que c'est le fantôme d'une propriété plus forte liée à la théorie des représentations de ces ensembles ordonnés. Dans cet exposé, j'expliquerai comment la démonstration de cette conjecture permet aussi d'obtenir une démonstration `presque combinatoire' de la propriété périodique des matrices de Coxeter de ces ensembles. https://cnrs.zoom.us/j/94236281873?pwd=LzIyV3F5Q0JtVzN4ZU0waW84M0pVUT09 Enumerative and analytic combinatorics Thursday April 21, 2022, 2PM, Salle 3052 Jessica Mulpas (Université Libre de Bruxelles) String C-group representations of some almost simple groups Abstract polytopes are a combinatorial abstraction of convex polytopes. When an abstract polytope is regular, that is when it is rich in symmetries (in a sense we will formalize), one can associate it with a presentation of its automorphism group with involutory generators called 'string C-group representation'. We present an algorithm to classify string C-group representations of finite groups. This algorithm enabled us to compute all string C-group representations for previously unattainable sporadic groups as well as to complete the classification for the O'Nan group. If time allows, we'll talk about some ways to obtain a string C-group representation for a given group from another by altering its rank (i.e. its number of involutory generators). https://u-paris.zoom.us/j/82996433359?pwd=YkJNTEFaRDE1QjMzUXp1a1poL1FRUT09 Enumerative and analytic combinatorics Thursday April 14, 2022, 2PM, Salle 3052 Alessandro Iraci (UQAM) Delta and Theta operators expansions Delta and Theta operators are two families of operators on symmetric functions that show remarkable combinatorial properties. Delta operators generalise the famous nabla operator by Bergeron and Garsia, and have been used to state the Delta conjecture, an extension of the famous shuffle theorem proved by Carlsson and Mellit. Theta operators have been introduced in order to state a compositional version of the Delta conjecture, with the idea, later proved successful, that this would have led to a proof via the Carlsson-Mellit Dyck path algebra. We are going to give an explicit expansion of certain instances of Delta and Theta operators when t=1 in terms of what we call gamma Dyck paths, generalising several results including the Delta conjecture itself, using interesting combinatorial properties of the forgotten basis of the symmetric functions. Enumerative and analytic combinatorics Thursday April 7, 2022, 2PM, Salle 3052 Ariane Carrance (CMAP) À la recherche du trisp brownien À quoi ressemble la structure fondamentale de notre espace-temps ? Dans cet exposé, une piste de réponse possible à cette question nous amènera à nous intéresser à des modèles aléatoires sur une famille particulière de complexes cellulaires, les trisps colorés. Enumerative and analytic combinatorics Thursday March 31, 2022, 11AM, IHP Seminaire Flajolet Philippe Biane, Sylvie Corteel, Marie Theret http://semflajolet.math.cnrs.fr/index.php/Main/HomePage Enumerative and analytic combinatorics Thursday March 17, 2022, 2PM, Salle 1007 Pooneh Afshari Joo Identités de partitions des nombres entiers à travers l’Algèbre commutative Nous allons etudier les identites de partitions en utilisant la relation entre les series generatrices des partitions et les series de Hilbert-Poincare des algebres graduees associees a un objet important de la geometrie algebrique : l’espace des arcs. En utilisant des ideaux differentiels, nous donnons deux nouveaux membres des identites de Rogers-Ramanujan. Ensuite, nous enoncons un theoreme qui nous mene a une nouvelle version des identites de Golnitz-Gordon. Un corollaire de ce theoreme nous donne une identite entre les overpartitons. Enfin, nous presentons un nouveau membre des identites de Gordon. Enumerative and analytic combinatorics Thursday March 10, 2022, 2PM, Salle 1007 Dan Betea (Université d'Angers) From Gumbel to Tracy–Widom via random (ordinary, plane, and cylindric plane) partitions We present a few natural (and combinatorial) measures on partitions, plane partitions, and cylindric plane partitions. We show how the extremal statistics of such measures, i.e. the distributions of the largest parts of the respective random objects, interpolate between the Gumbel distribution of classical statistics and the Tracy–Widom GUE distribution of random matrix theory, and do so in more than one way. These laws usually appear in opposite probabilistic contexts: the former distribution (Gumbel) appears universally in the study of extrema of iid random variables, the latter (Tracy–Widom) appears in the extrema of correlated systems (e.g. for the largest eigenvalue of random Hermitian matrices). All statistics also have a last passage percolation interpretation via the Robinson–Schensted–Knuth correspondence. Proofs rely on an interplay between algebraic combinatorics, mathematical physics, and complex analysis. The results are based on joint works with Jérémie Bouttier and Alessandra Occelli. Enumerative and analytic combinatorics Thursday February 24, 2022, 2PM, Salle 3052 et sur zoom Elba Garcia-Failde (IMJ-PRG Sorbonne Universite) Une dualité triple : symplectique, simple et libre Dans cet exposé, je présenterai trois transformations qui apparaissent dans des contextes très différents : des cartes combinatoires qui se simplifient, des cumulants qui se libèrent, et des x et y qui s’échangent symplectiquement dans la récurrence topologique. J'expliquerai comment réaliser toutes ces dualités par le biais d’une transformation universelle qui utilise les nombres de Hurwitz monotones doubles. Exprimer la transformation comme l’action d'un opérateur dans l'espace de Fock nous permet d'utiliser les techniques récentes développées par Bychkov, Dunin-Barkowski, Kazarian et Shadrin pour trouver des relations fonctionnelles reliant les séries génératrices des moments d'ordre supérieur et des cumulants libres, ce qui résout un problème ouvert posé par Collins, Mingo, Sniady et Speicher lors du développement de la théorie de second ordre qui généralise la transformée R de Voiculescu. Cela nous conduit à une théorie générale de la liberté qui prend en compte les corrections de genre supérieur qui apparaissent naturellement dans les deux autres contextes. Nous introduisons une notion de cumulants libres surfaciques à partir de la combinatoire du poset de permutations surfaciques (une généralisation des permutations partitionnées) qui capture les développements asymptotiques de tout ordre dans les modèles de matrices aléatoires avec invariance unitaire. Basé sur un travail en commun avec Gaëtan Borot, Severin Charbonnier, Felix Leid et Sergey Shadrin. Enumerative and analytic combinatorics Thursday February 17, 2022, 2PM, Salle 3052 et sur zoom Anna Vanden Wyngaerd (IRIF) Tiered tiers, polyominoes and Theta operators. In [Dugan-Glennon-Gunnells-Steingrimsson-2019], the authors introduce tiered trees to define combinatorial objects counting absolutely indecomposable representations of certain quivers, and torus orbits on certain homogeneous varieties. In our work, we use Theta operators, introduced in [D'Adderio-Iraci-VandenWyngaerd-Theta-2021], to give a symmetric function formula that enumerates these trees. We then formulate a general conjecture that extends this result, a special case of which might give some insight about how to formulate a unified Delta conjecture [Haglund-Remmel-Wilson-2018]. Joint work with Michele D'Adderio, Alessandro Iraci, Yvan LeBorgne and Marino Romero. https://cnrs.zoom.us/j/94236281873?pwd=LzIyV3F5Q0JtVzN4ZU0waW84M0pVUT09 Enumerative and analytic combinatorics Thursday February 10, 2022, 2PM, Salle 1007 Daniel Tamayo Permutree Sorting We define permutree sorting which generalizes the stack sorting and Coxeter sorting algorithms respectively due to Knuth and Reading. Given two disjoint subsets U and D of {2,…,n}, it consists of an algorithm that fails for a permutation if and only if there are integers i<j<k in [n] such that the permutation contains the pattern jki (resp. kij) if j is in U (resp. in D). We present this algorithm through automata that read reduced expressions and accept only those that form a specific structure within the weak order. This is joint work with Vincent Pilaud and Viviane Pons. Enumerative and analytic combinatorics Wednesday February 9, 2022, 2PM, Salle 3052 et sur zoom Journées De L'anr Combiné Anna Van Den Wyngaerd, David Wahiche, Corentin Henriet, Philippe Nadeau [14h-14h30] Tiered tiers, polyominoes and Theta operators. [14h30] Théorèmes de multiplication pour les partitions auto-conjuguées. [15h] Des poissons combattants pour une formule sur la distance dans le treillis de Tamari. [15h30] Algorithme de parking, polynômes quasisymétriques et calcul de Schubert. https://anr-combine.math.cnrs.fr/event-un.html Enumerative and analytic combinatorics Tuesday February 8, 2022, 2PM, Salle 3052 et sur zoom Journées De L'anr Combiné Andrea Sportiello, Joonas Turunen et Jehanne Dousse [14h] Many new conjectures on Fully-Packed Loop configurations. [14h45] Joonas Turunen - Combinatorial aspects of random planar triangulations of the disk coupled with an Ising model. [15h15] Partitions cylindriques et identités du type Rogers-Ramanujan. https://anr-combine.math.cnrs.fr/event-un.html Enumerative and analytic combinatorics Thursday February 3, 2022, 2PM, IHP Amphi Darboux Seminaire Flajolet Jiang Zeng et Marie Albenque http://semflajolet.math.cnrs.fr/index.php/Main/HomePage Enumerative and analytic combinatorics Thursday January 20, 2022, 2PM, Salle 3052 et sur zoom Noémie Cartier (Université de Paris-Saclay) Lattice properties of acyclic pipe dreams A pipe dream is a collection of pipes that trace the values of a permutation when passing through a sorting network. By choosing the sorting network and the permutation carefully, the set of reduced pipe dreams gives a realization of the Tamari lattice, a famous lattice quotient of the weak order. The talk will present a generalization of this result: if our sorting network respects a few specific properties, the set of reduced and acyclic pipe dreams of a permutation is a lattice quotient of an interval of the weak order. https://cnrs.zoom.us/j/94236281873?pwd=LzIyV3F5Q0JtVzN4ZU0waW84M0pVUT09 Enumerative and analytic combinatorics Thursday January 13, 2022, 2PM, Salle 3052 et sur zoom Eva Philippe Sweep polytopes and sweep oriented matroids Consider a configuration of n labeled points in a Euclidean space. Any linear functional gives an ordering of these points: an ordered partition that we call a sweep, because we can imagine its parts as the sets of points successively hit by a sweeping hyperplane. The set of all such sweeps forms a poset which is isomorphic to a polytope, called the sweep polytope. I will present several constructions of the sweep polytope, related to zonotopes, projections of permutahedra and monotone path polytopes of zonotopes. In a second part, I will present an abstract generalization of this structure in terms of oriented matroids. This is joint work with Arnau Padrol. https://cnrs.zoom.us/j/94236281873?pwd=LzIyV3F5Q0JtVzN4ZU0waW84M0pVUT09