Tullio Ceccherini-Silberstein

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This is an expostion of various aspects of amenability and paradoxical decompositions for groups, group actions and metric spaces. First, we review the formalism of pseudogroups, which is well adapted to stating the alternative of Tarski, according to which a pseudogroup without invariant mean gives rise to paradoxical decompositions, and to defining a(More)
The representation theory of the symmetric groups is a classical topic that, since the pioneering work of Frobenius, Schur and Young, has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained book provides a detailed introduction to the subject, covering classical topics such as the(More)
Let G be a finitely generated group, A a finite set of generators and K a subgroup of G. We call the pair (G, K) context-free if the set of all words over A that reduce in G to an element of K is a context-free language. When K is trivial, G itself is called context-free; context-free groups have been classified more than 20 years ago in celebrated work of(More)
For every infinite sequence ω = x1x2 . . ., with xi ∈ {0, 1}, we construct an infinite 4-regular graph Xω. 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(More)
A language L over a )nite alphabet is called growth-sensitive if forbidding any set of subwords F yields a sub-language L whose exponential growth rate is smaller than that of L. It is shown that every (essentially) ergodic non-linear context-free language of convergent type is growth-sensitive. “Ergodic” means that the dependency di-graph of the generating(More)
Extending the analogous result of Cannon andWagreich for the fundamental groups of surfaces, we show that, for the l-regular graphs Xl,m 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 (Floyd and Plotnick, 1994)) are reciprocal Salem(More)