一个涉及偏序集关联多面体的h-多项式与B型Narayana多项式的恒等式
An identity involving $h$-polynomials of poset associahedra and type B Narayana polynomials
AI总结：
本文针对偏序集关联多面体的h-多项式，通过将链状自治子偏序集替换为反链构造新偏序集，建立了其与B型Narayana多项式的恒等式，并由此推导出涉及Narayana多项式、Eulerian多项式和栈排序原像的多个恒等式。
摘要：
对于任意有限连通偏序集$P$，Galashin引入了一个简单的凸$(|P|-2)$维多面体$\mathscr{A}(P)$，称为偏序集关联多面体。设$P$为一个偏序集，其具有一个大小为$n$的链的真自治子偏序集$S$。对于$1\leq i \leq n$，令$P_i$为将$S$替换为大小为$i$的反链后从$P$得到的偏序集。我们证明了$\mathscr{A}(P)$的$h$-多项式可以用$\mathscr{A}(P_i)$的$h$-多项式和B型Narayana多项式表示。随后我们利用该恒等式推导出若干涉及Narayana多项式、Eulerian多项式以及栈排序原像的恒等式。
英文摘要：
For any finite connected poset $P$, Galashin introduced a simple convex $(|P|-2)$-dimensional polytope $\mathscr{A}(P)$ called the poset associahedron. Let $P$ be a poset with a proper autonomous subposet $S$ that is a chain of size $n$. For $1\leq i \leq n$, let $P_i$ be the poset obtained from $P$ by replacing $S$ by an antichain of size $i$. We show that the $h$-polynomial of $\mathscr{A}(P)$ can be written in terms of the $h$-polynomials of $\mathscr{A}(P_i)$ and type B Narayana polynomials. We then use the identity to deduce several identities involving Narayana polynomials, Eulerian polynomials, and stack-sorting preimages.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
