COMBINATORIAL HOPF ALGEBRAS OF SIMPLICIAL COMPLEXES

被引：14

作者：

Benedetti, Carolina ^{[1
]}

Hallam, Joshua ^{[2
]}

Machacek, John ^{[3
]}

机构：

[1] Fields Inst, Toronto, ON, Canada

[2] Wake Forest Univ, Dept Math & Stat, Winston Salem, NC 27109 USA

[3] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2016年 / 30卷 / 03期

关键词：

combinatorial Hopf algebra; quasi-symmetric functions; simplicial complex; colorings;

D O I：

10.1137/15M1038281

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a family of characters on this Hopf algebra. The characters of these combinatorial Hopf algebras give rise to symmetric functions that encode information about colorings of simplicial complexes and their f-vectors. We also use characters to give a generalization of Stanley's (-1)-color theorem. A q-analogue version of this family of characters is also studied.

引用

页码：1737 / 1757

页数：21

共 16 条

[1] Combinatorial Hopf algebras and generalized Dehn-Sommerville relations [J].