论文标题
$ p $ - 分区的多元相关性不平等
Multivariate correlation inequalities for $P$-partitions
论文作者
论文摘要
受Schur功能的LAM-Pylyavskyy不平等的动机，我们对Fishburn相关性不平等的多元概括对于POSET的线性扩展数量的数量。然后，我们对Daykin-Paterson不平等进行多元概括，证明了POSET的多项式订单的对数洞穴。我们还证明了Brightwell-Felsner-Trotter的跨产品不平等的多元$ P $ - 分区版本。证明是基于Ahlswede-daykin不平等的多元概括。
Motivated by the Lam--Pylyavskyy inequalities for Schur functions, we give a far reaching multivariate generalization of Fishburn's correlation inequality for the number of linear extensions of posets. We then give a multivariate generalization of the Daykin--Daykin--Paterson inequality proving log-concavity of the order polynomial of a poset. We also prove a multivariate $P$-partition version of the cross-product inequality by Brightwell--Felsner--Trotter. The proofs are based on a multivariate generalization of the Ahlswede--Daykin inequality.
