Words in Linear Groups, Random Walks, Automata and P-Recursiveness

Abstract

Fix a finite set $S\subset GL(k,\mathbb{Z})$. Denote by $a_n$ the number of products of matrices in $S$ of length $n$ that are equal to 1. We show that the sequence $\{a_n\}$ is not always P-recursive. This answers a question of Kontsevich.

10 pages, 1 figure

Cited by in corpus (1)

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