Computing the number of symmetric colorings of elementary Abelian groups

Given a finite group G and a positive integer r, an r-coloring of G is any mapping chi : G -> {1, ..., r}. Colorings chi and phi are equivalent if there exists g is an element of G such that chi(xg(-1)) = phi(x) for all x is an element of G. A coloring chi is symmetric if there exists g is an element of G such that chi(gx(-1)g) = chi(x) for every x is an element of G. We compute the number of symmetric r-colorings and the number of equivalence classes of symmetric r-colorings of an elementary Abelian p-group. (C) 2020 THE AUTHOR. Published by Elsevier BV on behalf of Faculty of Engineering,

Automated summary

This paper discusses the concept of r-colorings and symmetric r-colorings of finite groups, as well as calculates the number of symmetric r-colorings and the number of equivalence classes of symmetric r-colorings in elementary Abelian p-groups.