Fractals and Numeration » Publications

Papers with authors from both groups of the project

  • Non-stationary Markov partitions, flows on homogeneous spaces, and continued fractions
    P. Arnoux, V. Berthé, M. Minervino, W. Steiner, J. Thuswaldner. In preparation.
  • The S-adic Pisot conjecture on two letters
    V. Berthé, M. Minervino, W. Steiner, J. Thuswaldner.
    Topology Appl. 205 (2016), 47–57. arXiv, DOI
  • Geometry, dynamics, and arithmetic of S-adic shifts
    V. Berthé, W. Steiner, J. Thuswaldner. arXiv
  • Recognizability for sequences of morphisms
    V. Berthé, S. Steiner, J. Thuswaldner R. Yassawi. In preparation.
  • Brun algorithm and Ostrowki numeration
    V. Berthé, D. Krenn, M. R. Iacò. In preparation.
  • Topological properties of three-dimensional Rauzy fractals
    G. Conner, T. Jolivet, B. Loridant, J. Thuswaldner. In preparation
  • Linear recursive odometers and beta-expansions
    M. R. Iacò, W. Steiner, R. F. Tichy
    Unif. Distrib. Theory 11 (2016), no. 1, 175–186. arXiv, DOI
  • Rauzy fractals with countable fundamental group
    T. Jolivet, B. Loridant, J. Luo
    J. Fractal Geom. 1 (2014), no. 4, 427–447. arXiv
  • A numerical scale for non-locally connected continua
    T. Jolivet, B. Loridant, J. Luo
    Topology and its Applications 202 (2016), 21-39. arXiv
  • Geometrical models for reducible Pisot substitutions
    B. Loridant, M. Minervino. arXiv
  • Tilings for Pisot beta numeration
    M. Minervino, W. Steiner
    Indag. Math. (N.S.) 25 (2014), no. 4, 745–773. arXiv, HAL, DOI
  • The Geometry of non-unit Pisot substitutions
    M. Minervino, J. Thuswaldner
    Ann. Inst. Fourier (Grenoble) 64 (2014), no. 4, 1373-1417. DOI

Publications within the project

  • Characterization of the numbers which satisfy the height reducing property
    Shigeki Akiyama, Jörg M. Thuswaldner, Toufik Zaïmi
    Indagationes Mathematicae, 26 (2015), 24-27. arXiv
  • Comments on the height reducing property II
    Shigeki Akiyama, Jörg M. Thuswaldner, Toufik Zaïmi
    Indagationes Mathematicae 26 (2015), 28-39. arXiv
  • On the Pisot substitution conjecture
    Shigeki Akiyama, Marcy Barge, Valérie Berthé, Jeong-Yup Lee, Anne Siegel
    Mathematics of Aperiodic Order, J. Kellendonk, D. Lenz, J. Savinien (Eds)
    Progress in Mathematics (Birkhäuser), Vol. 309 (2015) 33--72.
  • Efficient Algorithms for Zeckendorf Arithmetic
    Connor Ahlbach, Jeremy Usatine, Christiane Frougny, and Nicholas Pippenger
    Fibonacci Quaterly, 51(3) (2013), 249-255
  • Euler’s divergent series and an elementary model in Statistical Physics
    Bill Allombert, Jean-Paul Allouche, Michel Mendès France
    Ars Math. Contemp. 12 (2017) 67-76.
  • On a formula of T. Rivoal
    Jean-Paul Allouche
    Annales Univ. Sci. Budapest., Sect. Comp. 40 (2013) 69-79. arXiv
  • A note on products involving zeta(3) and Catalan's constant
    Jean-Paul Allouche
    Ramanujan J. 37 (2015) 79-88. arXiv
  • Thue, Combinatorics on words, and conjectures inspired by the Thue-Morse sequence
    Jean-Paul Allouche
    J. Théorie des Nombres, Bordeaux 27 (2015) 375-388. arXiv
  • On a Golay-Shapiro-like sequence
    Jean-Paul Allouche
    Unif. Distrib. Theory 11 (2016) 205-210.
  • Paperfolding infinite products and the gamma function
    Jean-Paul Allouche
    J. Number Theory 148 (2015) 95-111. arXiv
  • Variations on an error sum function for the convergents of some powers of $e$
    Jean-Paul Allouche, Thomas Baruchel
    Integers 16 (2016) #A47. arXiv
  • Quasicrystals, model sets, and automatic sequences
    Jean-Paul Allouche, Yves Meyer
    C. R. Physique 15 (2014) 6-11. arXiv
  • Summation of rational series twisted by strongly B-multiplicative coefficients
    Jean-Paul Allouche, Jonathan Sondow
    Electronic J. Combinatorics 22 (2015), #1.59. arXiv
  • Beyond odious and evil
    Jean-Paul Allouche, Benoit Cloitre, Victor Shevelev
    Aequ. Math. 90 (2016) 341-353. arXiv
  • On some symmetric multidimensional continued fraction algorithms
    Pierre Arnoux, Sébastien Labbé
    Ergodic Theory and Dynamical Systems (2017) arXiv doi
  • An extremal problem in uniform distribution theory
    V. Balaz, M. R. Iacò, O. Strauch, S. Thonhauser, R. Tichy
    Uniform distribution theory, to appear.
  • On the regularity of the generalised golden ratio function
    Simon Baker, Wolfgang Steiner
    Bulletin of the London Mathematical Society, to appear. arXiv
  • Combinatorial and probabilistic properties of systems of numeration
    G. Barat, P. J. Grabner
    Ergodic Theory Dynam. Systems, 1-36 (2014).
  • Critical itineraries of maps with constant slope and one discontinuity
    Michael Barnsley, Wolfgang Steiner, Andrew Vince
    Math. Proc. Cambridge Philos. Soc. 157 (2014), no. 3, 547–565.
  • Diophantine approximation of Mahler numbers
    Jason P. Bell, Yann Bugeaud, Micheal Coons
    Proceedings of the London Mathematical Society 110 (2015) 1157-1206. arxiv
  • Uniform distribution of prime powers and sets of recurrence and van der Corput sets in Z^k
    V. Bergelson, G. Kolesnik, M. Madritsch, Y. Son, R. Tichy
    Israel J. 201 (2014) 729-760.
  • Beyond substitutive dynamical systems: S-adic expansions
    Valérie Berthé, Vincent Delecroix
    RIMS Lecture note `Kokyuroku Bessatu' B46 (2014) 81-123. arXiv
  • A combinatorial approach to products of Pisot substitutions
    Valérie Berthé, Jérémie Bourdon, Timo Jolivet, Anne Siegel
    Ergodic Theory and Dynamical Systems 36 (2016) 1757-1794. arXiv
  • Generating Discrete Planes with Substitutions
    Valérie Berthé, Jérémie Bourdon, Timo Jolivet, Anne Siegel
    In Proceedings WORDS 2013, Lecture Notes in Computer Science 8079 (2013), 58-70. DOI
  • Factor Complexity of S-adic sequences generated by the Arnoux-Rauzy-Poincaré Algorithm
    Valérie Berthé, Sébastien Labbé
    Adv. in Appl. Math., 63 (2015), 90--130. arXiv, DOI
  • On-line multiplication and division in real and complex bases
    Marta Brzicová, Christiane Frougny, Edita Pelantová, and Milena Svobodová
    Proceedings of IEEE ARITH 23, I.E.E.E. Computer Society Press (2016).
  • On-line algorithms for multiplication and division in real and complex numeration systems
    Marta Brzicová, Christiane Frougny, Edita Pelantová, and Milena Svobodová
    Preprint. arXiv
  • Permutations and negative beta-shifts
    Émilie Charlier, Wolfgang Steiner
    Preprint. arXiv
  • Self-affine manifolds
    Gregory R. Conner and Jörg M. Thuswaldner
    Advances in Mathematics 289 (2016) 725-783. [ | arXiv]]
  • Mixed labyrinth fractals
    L.L.Cristea, B.Steinsky
  • On the length of arcs in labyrinth fractals
    L.L. Cristea, G. Leobacher
  • Uniform distribution with respect to density
    L.L. Cristea, M. Pasteka
    Uniform Distribution Theory, to appear.
  • Balancedness of Arnoux-Rauzy and Brun words
    Vincent Delecroix, Tomáš Hejda, Wolfgang Steiner
    In Proceedings WORDS 2013, Lecture Notes in Computer Science 8079 (2013), 119-131. arXiv, HAL, DOI
  • Unimodular Pisot substitutions and domain exchanges
    Fabien Durand, Samuel Petite
  • Eigenvalues of minimal Cantor systems
    Fabien Durand, Alexander Frank, Alejandro Maass
  • Factor and palindromic complexity of Thue-Morse's avatars
    Christiane Frougny, Karel Klouda
    Acta Polytechnica, 53(6) (2013), 868-871
  • Beta-representations of 0 and Pisot numbers
    Christiane Frougny, Edita Pelantová
    Preprint. arXiv
  • Minimal Digit Sets for Parallel Addition in Non-Standard Numeration Systems
    Christiane Frougny, Edita Pelantová, and Milena Svobodová
    Journal of Integer Sequences, 16 (2013), Article 13.2.17
  • k-block parallel addition versus 1-block parallel addition in non-standard numeration systems
    Christiane Frougny, Pavel Heller, Edita Pelantová, and Milena Svobodová
    Theoretical Computer Science 543 (2014), 52-67
  • Poincaré functional equations, harmonic measures on Julia sets, and fractal zeta functions
    P. J. Grabner
    In Fractal Geometry and Stochastics V (edited by C. Bandt, K. Falconer, and M. Zähle), vol. 70 of Progress in Probability. Birkhäuser Verlag, Basel, pp. 157--174.
  • Multiple tilings associated to d-Bonacci beta-expansions
    Tomáš Hejda
    Preprint. arXiv
  • Beta-expansions of rational numbers in quadratic Pisot bases
    Tomáš Hejda, Wolfgang Steiner
    Acta Arithmetica, to appear. arXiv
  • Spectral properties of cubic complex Pisot units
    Tomáš Hejda, Edita Pelantová
    Mathematics of Computation 85 (2016), no. 297, 401–421. arXiv
  • Ergodic properties of beta-adic Halton sequences
    M. Hofer, M. R. Iacò, R. Tichy,
    Ergodic theory and dynamical systems, 35 (2015), 895-909.
  • Measure density for set decompositions and uniform distribution
    M.R. Iacò, M. Pasteka, R. Tichy
    Rend. Circ. Mat. Palermo 64 (2015), no. 2, 323–339.
  • Distribution functions, extremal limits and optimal transport
    M. R. Iacò, S. Thonhauser, R. Tichy
    Indagationes Mathematicae 26 (2015), 823-841.
  • Undecidability in self-affine sets and multi-tape automata
    Timo Jolivet, Jarkko Kari
    MFCS 2014
  • A number theoretic problem on the distribution of polynomials with bounded roots
    P. Kirschenhofer, P. Weitzer
    Integers 15 (2015) A10.
  • Finite beta-expansions with negative bases
    Zuzana Krčmáriková, Wolfgang Steiner, Tomáš Vávra
    Acta Math. Hungar., to appear. arXiv
  • On the Number of Multi-Base Representations of an Integer
    Daniel Krenn, Dimbinaina Ralaivaosaona, Stephan Wagner
    In DMTCS Proceedings for AofA'14 (2014), pp. 229–240. HAL
  • Multi-Base Representations of Integers: Asymptotic Enumeration and Central Limit Theorems
    Daniel Krenn, Dimbinaina Ralaivaosaona, Stephan Wagner
    Appl. Anal. Discrete Math. 9 (2015), no. 2, 285–312.
  • Shift Radix Systems - A Survey
    Peter Kirschenhofer, Jörg Thuswaldner
    RIMS Lecture note `Kokyuroku Bessatu' B46 (2014). arXiv
  • A d-dimensional extension of Christoffel words
    Sébastien Labbé, Christophe Reutenauer
    Discrete & Computational Geometry, 54 (2015) 152-181. arXiv doi
  • Topological properties of a class of cubic Rauzy fractals
    Benoît Loridant
    Osaka Journal of Mathematics 53 (2016), 161-219. arXiv
  • On cut sets of attractors of iterated function systems
    Benoît Loridant, Jun Luo, Tarek Sellami, Jörg Thuswaldner
    Proceedings of the American Mathematical Society, 144 (2016) no. 10, pp. 4341-4356. arXiv
  • Construction of normal numbers via generalized prime power sequences
    M. Madritsch, R. Tichy
    Journal of Integer Sequences, Vol.16, (2013).
  • Normality in Pisot Numeration Systems
    Adrian-Maria Scheerer
    Ergodic Theory Dynam. Systems 37 (2017), 664-672. arXiv