论文标题
删除收缩的长度精确序列，用于彩色对称同源性
A deletion-contraction long exact sequence for chromatic symmetric homology
论文作者
论文摘要
机组人员和Spirklt将Stanley的色度对称功能概括为顶点加权图。将色度对称函数扩展到顶点加权图的主要动机之一是在这种情况下存在删除 - 收集关系，众所周知，该关系适用于色多项式，但不能适用于色对称函数。在本文中，我们发现了它们的新不变式的分类，将色素对称同源性的定义扩展到了顶点加权图。我们证明了用于色度对称同源性的缺失 - 收缩长精确序列，该序列提高了用于扩展机组人员和Spirklt的删除 - 收集关系。此外，新的分类提供了一个有用的计算工具，并允许我们回答Chandler，Sazdanovic，Stella和YIP的两个问题。特别是，我们证明，对于具有$ n $顶点的图G，具有非零同源性的最大索引并不比$ n $ -1。
Crew and Spirklt generalize Stanley's chromatic symmetric function to vertex-weighted graphs. One of the primary motivations for extending the chromatic symmetric function to vertex-weighted graphs is the existence of a deletion-contraction relation in this setting, which, as known, holds for the chromatic polynomial, but doesn't hold for the chromatic symmetric function. In this paper we find a categorification of their new invariant extending the definition of chromatic symmetric homology to vertex-weighted graphs. We prove the existence of a deletion-contraction long exact sequence for chromatic symmetric homology which lifts the deletion-contraction relation that holds for the extension of Crew and Spirklt. Moreover, the new categorification gives a useful computational tool and allow us to answer two questions left open by Chandler, Sazdanovic, Stella and Yip. In particular, we prove that, for a graph G with $n$ vertices, the maximal index with nonzero homology is not greater that $n$ - 1. Moreover, we show that the homology is non-trivial for all the indices between the minimum and the maximum with this property.
