On h-Polynomials of Hibi rings

Abstract: Let $L$ be a finite distributive lattice. By a theorem of Birkhoff, $L$ is the ideal lattice $\mathcal{I}(P)$ of its subposet $P$ of join-irreducible elements. Let $P=\{p_1,\ldots,p_n\}$ and let $R=K[t,z_1,\ldots,z_n]$ be the polynomial ring in $n+1$ variables over a field $K.$ The {\em Hibi ring} associated with $L$, denoted by $R[L]$, is the subring of $R$ generated by the monomials $u_{\alpha}=t\prod_{p_i\in \alpha}z_i$ where $\alpha\in L$. In this talk we will state the Charney–Davis-Stanley(CDS) conjecture and we will prove that CDS conjecture is true for all Gorenstein Hibi rings of regularity $4$.

commutative algebraalgebraic topologycombinatorics

Audience: researchers in the topic

Applications of Combinatorics in Algebra, Topology and Graph Theory

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