论文标题
完整的多片式对称函数
A complete multipartite basis for the chromatic symmetric function
论文作者
论文摘要
在对称函数的矢量空间中，基本对称函数基础的元素是（最高因素）群集脱节联盟的色度对称函数。我们考虑他们的图形补充，功能$ \ {r_λ：λ\ text {一个整数分区} \} $定义为完整多部分图的色度对称函数。此基础是Penaguiao [21]首先引入的。我们为$r_λ$和单一对称函数之间的基本变化公式的系数提供了组合解释，我们表明，当在$ r $ $ r $中扩展到$ r $ - basis numumate $ r $ g $的形式和tutte对称函数的系数中，$ r $ the-basis num-basis numumate unumate $ r $ the $ r $ g $ no-bbasis num-basis numage numumate $ r $ g $ n cobsis $ r $ a $ v（g）$ v（g）$ v（g）c。
In the vector space of symmetric functions, the elements of the basis of elementary symmetric functions are (up to a factor) the chromatic symmetric functions of disjoint unions of cliques. We consider their graph complements, the functions $\{r_λ: λ\text{ an integer partition}\}$ defined as chromatic symmetric functions of complete multipartite graphs. This basis was first introduced by Penaguiao [21]. We provide a combinatorial interpretation for the coefficients of the change-of-basis formula between the $r_λ$ and the monomial symmetric functions, and we show that the coefficients of the chromatic and Tutte symmetric functions of a graph $G$ when expanded in the $r$-basis enumerate certain intersections of partitions of $V(G)$ into stable sets.
