3 problems

Let $\Gamma=\langle S\mid R\rangle$ be a group with finite generating set $S$, and let … be its cogrowth series, where $\psi_n$ counts words of length $n$ in the alphabet…

Cogrowth formula for non-negative functions. Fix $2\le c\le d$ and $3\le d$, and let $0\ne f\colon V(\mathbb{T}_{c,d})\to\mathbb{R}_{\ge 0}$ be a non-negative function on the verti…

Let $S$ be a finitely generated monoid. Its global cogrowth is maximal when the global cogrowth rate equals the cardinality of a chosen finite generating set. Left amenable means t…