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Let $Delta$ be a one-dimensional simplicial complex. Let $I_Delta$ be the Stanley-Reisner ideal of $Delta$. We prove that for all $s ge 1$ and all intermediate ideals $J$ generated by $I_Delta^s$ and some minimal generators of $I_Delta^{(s)}$, we have $${rm reg} J = {rm reg} I_Delta^s = {rm reg} I_Delta^{(s)}.$$
The goal of the present paper is the study of some algebraic invariants of Stanley-Reisner rings of Cohen-Macaulay simplicial complexes of dimension $d - 1$. We prove that the inequality $d leq mathrm{reg}(Delta) cdot mathrm{type}(Delta)$ holds for a
In this article we associate to every lattice ideal $I_{L,rho}subset K[x_1,..., x_m]$ a cone $sigma $ and a graph $G_{sigma}$ with vertices the minimal generators of the Stanley-Reisner ideal of $sigma $. To every polynomial $F$ we assign a subgraph
In this article, we prove that for several classes of graphs, the Castelnuovo-Mumford regularity of symbolic powers of their edge ideals coincide with that of their ordinary powers.
In this article, we study the regularity of integral closure of powers of edge ideals. We obtain a lower bound for the regularity of integral closure of powers of edge ideals in terms of induced matching number of graphs. We prove that the regularity
We consider simplicial complexes admitting a free action by an abelian group. Specifically, we establish a refinement of the classic result of Hochster describing the local cohomology modules of the associated Stanley--Reisner ring, demonstrating tha