论文标题
P分区生成功能之间的积极性
Positivity among P-partition generating functions
论文作者
论文摘要
我们在一对标记的POSET上寻求简单的条件，以确定其$（p，ω）$ - 分区枚举者的差异为$ f $ - 阳性，即Gessel的基本基础为正面。这是在一对偏斜形状上发现条件的广泛研究问题的准对称类似物，该问题确定何时其偏斜舒尔函数的差异是Schur阳性的。我们确定了$ f $ potitivity的必要条件和单独的条件，并表明合并POSETS的广泛操作可保留阳性属性。我们以poset的类别结束，我们的条件既是必要又足够的条件。
We seek simple conditions on a pair of labeled posets that determine when the difference of their $(P,ω)$-partition enumerators is $F$-positive, i.e., positive in Gessel's fundamental basis. This is a quasisymmetric analogue of the extensively studied problem of finding conditions on a pair of skew shapes that determine when the difference of their skew Schur functions is Schur-positive. We determine necessary conditions and separate sufficient conditions for $F$-positivity, and show that a broad operation for combining posets preserves positivity properties. We conclude with classes of posets for which we have conditions that are both necessary and sufficient.
