elementary 基中色谱对称函数下界研究
组合数学
2026-02-18 v2
摘要
Tatsuyuki Hikita最近利用概率方法证明了Stanley--Stembridge猜想，表明单位区间图的色谱对称函数是正的。寻找这些系数的组合解释仍是一个主要的开放问题。一种方法是寻找Gasharov的-tableau子集的组合解释。为了这一目标，我们引入了强大的-tableau的集合，并用于找到的各种系数的组合解释。我们推测，强-tableau的集合给出了的系数的下界。此外，我们表明强-tableau和Shareshian--Wachs inversion统计量在Hikita的结果证明中自然出现。
引用
@article{arxiv.2509.02841,
title = {Toward Lower Bounds for Chromatic Symmetric Functions in the Elementary Basis},
author = {Isaiah Siegl},
journal= {arXiv preprint arXiv:2509.02841},
year = {2026}
}
备注
In a previous version, we conjectured that powerful $P$-tableaux give an upper bound for the $e$-coefficients of chromatic symmetric functions of incomparability graphs of natural unit interval orders. An anonymous reviewer showed that the poset corresponding to the reverse Hessenberg function (0,0,1,1,2,3,4,6) gives a counterexample to this conjecture