Tullio Ceccherini-Silberstein
Sapienza University of Rome
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Annales de l'Institut Fourier | 1999
Tullio Ceccherini-Silberstein; Antonio Machì; Fabio Scarabotti
© Annales de l’institut Fourier, 1999, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Archive | 2008
Tullio Ceccherini-Silberstein; Fabio Scarabotti; Filippo Tolli
Part I. Preliminaries, Examples and Motivations: 1. Finite Markov chains 2. Two basic examples on Abelian groups Part II. Representation Theory and Gelfand Pairs: 3. Basic representation theory of finite groups 4. Finite Gelfand pairs 5. Distance regular graphs and the Hamming scheme 6. The Johnson Scheme and the Laplace-Bernoulli diffusion model 7. The ultrametric space Part III. Advanced theory: 8. Posets and the q-analogs 9. Complements on representation theory 10. Basic representation theory of the symmetric group 11. The Gelfand Pair (S2n, S2 o Sn) and random matchings Appendix 1. The discrete trigonometric transforms Appendix 2. Solutions of the exercises Bibliography Index.
Transactions of the American Mathematical Society | 2002
Tullio Ceccherini-Silberstein; Wolfgang Woess
A language L over a finite alphabet E is called growth-sensitive if forbidding any set of subwords F yields a sublanguage L F whose exponential growth rate is smaller than that of L. It is shown that every ergodic unambiguous, nonlinear context-free language is growth-sensitive. Ergodic means for a context-free grammar and language that its dependency di-graph is strongly connected. The same result as above holds for the larger class of essentially ergodic context-free languages, and if growth is considered with respect to the ambiguity degrees, then the assumption of unambiguity may be dropped. The methods combine a construction of grammars for 2-block languages with a generating function technique regarding systems of algebraic equations.
arXiv: Group Theory | 2002
Laurent Barthold; Tullio Ceccherini-Silberstein
Extending the analogous result of Cannon and Wagreich for the fundamental groups of surfaces, we show that, for the l-regular graphs Xl,m associated to regular tessellations of hyperbolic plane by m-gons, the denominators of the growth series (which are rational and were computed by Floyd and Plotnick [FP94]) are reciprocal Salem polynomials. As a consequence, the growth rates of these graphs are Salem numbers. We also prove that these denominators are essentially irreducible (they have a factor of X + 1 when m ≡ 2 mod 4; and when l = 3 and m ≡ 6 mod 12, for instance, they have a factor of X −X +1). We then derive some regularity properties for the coefficients an of the growth series: they satisfy Kλ − R < an < Kλ n + R for some constants K, R > 0, λ > 1.AbstractExtending the analogous result of Cannon and Wagreich for the fundamental groups of surfaces, we show that, for the ℓ-regular graphs
European Journal of Combinatorics | 2012
Ievgen Bondarenko; Tullio Ceccherini-Silberstein; Alfredo Donno; Volodymyr Nekrashevych
Theoretical Computer Science | 2008
Tullio Ceccherini-Silberstein; Michel Coornaert
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LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES | 2013
Tullio Ceccherini-Silberstein; Fabio Scarabotti; Filippo Tolli
European Journal of Combinatorics | 2012
Tullio Ceccherini-Silberstein; Wolfgang Woess
associated to regular tessellations of the hyperbolic plane by m-gons, the denominators of the growth series (which are rational and were computed by Floyd and Plotnick) are reciprocal Salem polynomials. As a consequence, the growth rates of these graphs are Salem numbers. We also prove that these denominators are essentially irreducible (they have a factor of X + 1 when m ≡ 2 mod 4; and when ℓ = 3 and m ≡ 4 mod 12, for instance, they have a factor of X2 − X + 1). We then derive some regularity properties for the coefficients fn of the growth series: they satisfy Kλn − R < fn < Kλn + R for some constants K, R < 0, λ < 1.
Theoretical Computer Science | 2003
Tullio Ceccherini-Silberstein; Antonio Machì; Fabio Scarabotti
For every infinite sequence ω = x 1 x 2 ? , with x i ? { 0 , 1 } , we construct an infinite 4-regular graph X ω . These graphs are precisely the Schreier graphs of the action of a certain self-similar group on the space { 0 , 1 } ∞ . We solve the isomorphism and local isomorphism problems for these graphs, and determine their automorphism groups. Finally, we prove that all graphs X ω have intermediate growth.
Nonlinearity | 2012
Tullio Ceccherini-Silberstein; Michel Coornaert
Let A be a set and let G be a group, and equip A^G with its prodiscrete uniform structure. Let @t:A^G->A^G be a map. We prove that @t is a cellular automaton if and only if @t is uniformly continuous and G-equivariant. We also give an example showing that a continuous and G-equivariant map @t:A^G->A^G may fail to be a cellular automaton when the alphabet set A is infinite.