论文标题
$ P $阵列的水晶分析
A Crystal Analysis of $P$-Arrays
论文作者
论文摘要
Gasharov引入了称为$ p $ - 阵列的组合对象，以证明$ s $ potititive of（3+1） - free Posets的无与伦比性图的色度对称函数。我们在$ p $阵列的集合上定义了一个带有一些附加公理的有向彩色图。 Crystal的组成部分具有$ S $阳性的字符，从而完善了Gasharov的$ S $ - 阳性定理，以及Shareshian和Wachs。水晶暗示了Robinson-Schensted对应关系的可能概括应用于$ P $ - 阵列。
Gasharov introduced the combinatorial objects known as $P$-arrays to prove $s$-positivity for the chromatic symmetric functions of incomparability graphs of (3+1)-free posets. We define a crystal, a directed colored graph with some additional axioms, on the set of $P$-arrays. The components of the crystal have $s$-positive characters, thereby refining the $s$-positivity theorems of Gasharov, as well as Shareshian and Wachs. The crystal hints at a possible generalization of the Robinson-Schensted correspondence applied to $P$-arrays.
