论文标题
色度对称函数的非相对阳性
Non-Schur-positivity of chromatic symmetric functions
论文作者
论文摘要
我们为图形的色彩对称函数的每个Schur系数提供了一个公式，以特殊的RIM钩小小的小报。该公式可用于确认图形的色度对称函数的非距离阳性，尤其是在斯坦利的稳定分区方法不起作用的情况下。作为应用，我们确定Schur阳性风扇图和Schur阳性完整三方图。我们表明，如果$ M $ -VERTEX周期将$ n $叶子添加到普通顶点获得的任何鱿鱼图，如果$ m \ ne 2n-1 $，则构成schur schur均不阳性，并且猜测也不是$ m = 2n-1 $的鱿鱼图。
We provide a formula for every Schur coefficient in the chromatic symmetric function of a graph in terms of special rim hook tabloids. This formula is useful in confirming the non-Schur positivity of the chromatic symmetric function of a graph, especially when Stanley's stable partition method does not work. As applications, we determine Schur positive fan graphs and Schur positive complete tripartite graphs. We show that any squid graph obtained by adding $n$ leaves to a common vertex on an $m$-vertex cycle is not Schur positive if $m\ne 2n-1$, and conjecture that neither are the squid graphs with $m=2n-1$.
