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. [http://arxiv.org/abs/1402.3000 | arXiv]]
- Mixed labyrinth fractals
L.L.Cristea, B.Steinsky
Preprint.
- On the length of arcs in labyrinth fractals
L.L. Cristea, G. Leobacher
Preprint.
- 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
arXiv
- Eigenvalues of minimal Cantor systems
Fabien Durand, Alexander Frank, Alejandro Maass
arXiv
- 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