"Natural extension of arithmetic algorithms and S-adic system". July 20～24, 2015. edited by Shigeki Akiyama. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / In this survey we will introduce a necessary and sufficient condition that a Bratteli-Vershik adic system is uniquely ergodic.
Downarowicz and Maass (2008) have shown that every Cantor minimal homeomorphism with finite topological rank K>1 is expansive. Bezuglyi et al (2009) extended the result to non-minimal cases. On the other hand, Gambaudo and Martens (2006) had expressed all Cantor minimal continuous surjections as the inverse limit of graph coverings. In this paper, ...
Published in Functional Analysis and Its Applications
We describe the full exit boundary of random walks on homogeneous trees, in particular, on free groups. This model exhibits a phase transition; namely, the family of Markov measures under study loses ergodicity as a parameter of the random walk changes. The problem under consideration is a special case of the problem of describing the invariant (ce...
Published in Milan Journal of Mathematics
In a recent paper, F. Boca investigates the AF algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathfrak{A}}}$$\end{document} associated with the Farey-Stern-...
Une nouvelle approche pour la théorie des représentations du groupe symétrique a été développée par Okounkov et Vershik ; elle fournit un éclairage différent sur le sujet par rapport aux approches « traditionnelles ». Par ailleurs, cette méthode vise à établir un cadre reproductible pour étudier les représentations d'autres chaînes de groupes et d'...
Published in Southeast Asian Bulletin of Mathematics
Brauer’s centerlizer algebras have a basis consisting of undirected graphs. Signed Brauer’s algebras have a basis consisting of directed graphs, which generalizes Brauer’s algebras. In this paper, we compute a complete set of matrix units of Signed Brauer’s algebras.
Published in Journal of Fourier Analysis and Applications
In this paper we introduce new techniques for the efficient computation of a Fourier transform on a finite group. We use the decomposition of a group into double cosets and a graph theoretic indexing scheme to derive algorithms that generalize the Cooley-Tukey FFT to arbitrary finite group. We apply our general results to special linear groups and ...
