Chromatic classical symmetric functions

被引：7
|
作者：
Cho, Soojin [1 ]
van Willigenburg, Stephanie [2 ]
机构：
[1] Ajou Univ, Dept Math, Suwon 443749, South Korea
[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
来源：
JOURNAL OF COMBINATORICS | 2018年 / 9卷 / 02期
基金：
新加坡国家研究基金会;
关键词：
Chromatic symmetric function; complete graph; elementary symmetric function; skew Schur function;
D O I：
10.4310/JOC.2018.v9.n2.a8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note we classify when a skew Schur function is a positive linear combination of power sum symmetric functions. We then use this to determine precisely when any scalar multiple of a skew Schur function is the chromatic symmetric function of some graph. From here we are able to prove that of the classical bases for symmetric functions only certain scalar multiples of the elementary symmetric functions can be realised as the chromatic symmetric function of some graph, namely a particular union of complete graphs.
引用
收藏
页码：401 / 409
页数：9
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