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

共 50 条

[31] Modular Symmetries, Threshold Corrections and Moduli for Z2 x Z2 Orbifolds
Bailin, D.
Love, A.
Sabra, W. A.
Thomas, S.
Comptes Rendus De L'Academie Des Sciences. Serie I, Mathematique, 1994, 319
[32] Intersecting D-branes on shift Z2 x Z2 orientifolds
Blumenhagen, Ralph
Plauschinn, Erik
JOURNAL OF HIGH ENERGY PHYSICS, 2006, (08):
[33] Towards machine learning in the classification of Z2 x Z2 orbifold compactifications
Faraggi, A. E.
Harries, G.
Percival, B.
Rizos, J.
6TH SYMPOSIUM ON PROSPECTS IN THE PHYSICS OF DISCRETE SYMMETRIES - DISCRETE 2018, 2020, 1586
[34] Minimal extension of tribimaximal mixing and generalized Z2 x Z2 symmetries
Gupta, Shivani
Joshipura, Anjan S.
Patel, Ketan M.
PHYSICAL REVIEW D, 2012, 85 (03):
[35] Z2 x Z2 symmetry and Z4 Berry phase of bosonic ladders
Kuno, Yoshihito
Hatsugai, Yasuhiro
PHYSICAL REVIEW A, 2023, 108 (01)
[36] Grand unification of flavor by orbifold twisting Z2 and Z2 x Z12
Kim, JE
FIRST INTERNATIONAL CONFERENCE ON STRING PHENOMENOLOGY, 2003, : 173 - 178
[37] Z2 x Z2 generalizations of N=2 super Schrodinger algebras and their representations
Aizawa, N.
Segar, J.
JOURNAL OF MATHEMATICAL PHYSICS, 2017, 58 (11)
[38] Nonsmoothable actions of Z2 x Z2 on spin four-manifolds
Kato, Yuya
TOPOLOGY AND ITS APPLICATIONS, 2022, 307
[39] Classification of the chiral Z2 X Z2 fermionic models in the heterotic superstring
Faraggi, AE
Kounnas, C
Nooij, SEM
Rizos, J
NUCLEAR PHYSICS B, 2004, 695 (1-2) : 41 - 72
[40] Modular Symmetries, Threshold Corrections and Moduli for Z2 x Z2 Orbifolds
Bailin, D.
Love, A.
Sabra, W. A.
Thomas, S.
Mathematical and Computer Modelling (Oxford), 21 (05):

← 1 2 3 4 5 →