The orbit algebra of a permutation group with polynomial profile is Cohen-Macaulay

Justine Falque, Nicolas M. Thiéry

Let $G$ be a group of permutations of a denumerable set $E$. The profile of $G$ is the function ${\varphi }_G$ which counts, for each $n$, the (possibly infinite) number ${\varphi }_G(n)$ of orbits…