Queer对偶等价图
Queer dual equivalence graphs
摘要：
我们介绍了一个新的范式证明舒尔$P$ -积极的。推广对偶等价，我们给出了一个公理化的定义，即一个对象集上的对合族是一个奇异对偶等价，并且证明了只要这样的对合族存在，基本拟对称生成函数是Schur $P$ -正的.与移位对偶等价相反，当奇异对合被省略时，奇异对偶等价对合仅限于对偶等价。我们突出这两个推广之间的差异与一个新的应用程序的产品舒尔$P$ -功能。
英文摘要：
We introduce a new paradigm for proving the Schur $P$-positivity. Generalizing dual equivalence, we give an axiomatic definition for a family of involutions on a set of objects to be a queer dual equivalence, and we prove whenever such a family exists, the fundamental quasisymmetric generating function is Schur $P$-positive. In contrast with shifted dual equivalence, the queer dual equivalence involutions restrict to a dual equivalence when the queer involution is omitted. We highlight the difference between these two generalization with a new application to the product of Schur $P$-functions.
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