Counting symmetric colorings of G x Z2

被引：1

作者：

Phakathi, Jabulani ^{[1
]}

Singh, Shivani ^{[1
]}

Zelenyuk, Yevhen ^{[1
]}

Zelenyuk, Yuliya ^{[1
]}

机构：

[1] Univ Witwatersrand, Sch Math, Private Bag 3, ZA-2050 Johannesburg, South Africa

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2019年 / 18卷 / 10期

关键词：

Finite Abelian group; symmetric coloring; equivalent colorings; Mobius function; dihedral group;

D O I：

10.1142/S0219498819501998

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a finite group and let r is an element of N. An r-coloring of G is any mapping chi : G -> {1, . . . ,r}. A coloring chi is symmetric if there is g is an element of G such that chi(gx(-1)g) = chi(x) for every x is an element of G. We show that if G is Abelian and f(r) is the polynomial representing the number of symmetric r-colorings of G, then the number of symmetric r-colorings of G x Z(2) is f(r(2)). We also extend this result to the dihedral group D(G).

引用

页数：7

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