2025/03/04 by Ramón H. Ruiz-Medina, Ruiz-Medina, Ramón H.
Computer Science · Mathematics · #semigroups and automata theory #Rings, Modules, and Algebras #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2503.03772
A set with a group action is referred to as a G-set, and the set of functions that commute with this action forms a monoid under function composition. This paper examines the case where the G-set is finite, which implies that the monoid of G-equivariant functions is also finite. The document provides formulas for calculating the cardinality of this monoid, its group of units, and explores special cases of G-equivariant functions, known as fixing elementary collapsings. All of these results are expressed in terms of specific properties of the G-set, including the number of orbits and certain indices of the subgroups acting as stabilizers.