Signed differential posets and sign-imbalance

带符号偏序集多面体

Signed Poset Polytopes

本文定义并研究带符号序多面体与带符号链多面体，给出其凸包和半空间表示、幺模三角剖分、$h^*$-多项式及Gorenstein性质刻画。

符号不平衡、线性扩张的奇偶性与高度2偏序集的复杂性

Complexity of sign imbalance, parity of linear extensions, and height 2 posets

该研究聚焦高度2偏序集这一典型情形，证明了偏序集符号不平衡及线性扩张奇偶性相关的复杂性结果，并对Chan和Pak近期提出的相关猜想进行了探讨。

带符号偏序集的根半群环与权半群环

Root and weight semigroup rings for signed posets

本文研究带符号偏序集的根半群环与权半群环，给出其环面理想的生成元和Gröbner基，并刻画完全交集情形，推广了多个已有结果。

Some results on counting linearizations of posets

In section 1 we consider a 3-tuple $S=(|S|,\preccurlyeq,E)$ where $|S|$ is a finite set, $\preccurlyeq$ a partial ordering on $|S|,$ and $E$ a set of unordered pairs of distinct members of $|S|,$ and study, as a function of $n\geq 0,$ the number of maps $φ:|S|\to\{1,\dots,n\}$ which are both isotone with respect to the ordering $\preccurlyeq,$ and have the property that $φ(x)\neq φ(y)$ whenever $\{x,y\}\in E.$ We prove a number-theoretic result about this function, and use it in section 7 to recover a ring-theoretic identity of G. P. Hochschild. In section 2 we generalize a result of R. Stanle…

Some remarks on sign-balanced and maj-balanced posets

Let P be a poset with elements 1,2,...,n. We say that P is sign-balanced if exactly half the linear extensions of P (regarded as permutations of 1,2,...,n) are even permutations, i.e., have an even number of inversions. This concept first arose in the work of Frank Ruskey, who was interested in the efficient generation of all linear extensions of P. We survey a number of techniques for showing that posets are sign-balanced, and more generally, computing their "imbalance." There are close connections with domino tilings and, for certain posets, a "domino generalization" of Schur functions due t…