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pro vyhledávání: '"Fakhari, S."'
Let G be a finite simple graph and let indm(G) and ordm(G) denote the induced matching number and the ordered matching number of G, respectively. We characterize all bipartite graphs G with indm(G) = ordm(G). We establish the Castelnuovo-Mumford regu
Externí odkaz:
http://arxiv.org/abs/2405.06781
Autor:
Fakhari, S. A. Seyed
We prove some inequalities regarding the Castelnuovo--Mumford regularity of symbolic powers and integral closure of powers of monomial ideals.
Externí odkaz:
http://arxiv.org/abs/2401.12446
Autor:
Fakhari, S. A. Seyed
Let $\mathbb{K}$ be a field and $S=\mathbb{K}[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over $\mathbb{K}$. Assume that $I$ is a squarefree monomial ideal of $S$. For every integer $k\geq 1$, we denote the $k$-th squarefree power of $I$
Externí odkaz:
http://arxiv.org/abs/2309.13892
Autor:
Fakhari, S. A. Seyed
Assume that $G$ is a graph with cover ideal $J(G)$. For every integer $k\geq 1$, we denote the $k$-th symbolic power of $J(G)$ by $J(G)^{(k)}$. We provide a sharp upper bound for the regularity of $J(G)^{(k)}$ in terms of the star packing number of $
Externí odkaz:
http://arxiv.org/abs/2306.14420
Autor:
Fakhari, S. A. Seyed
Assume that $G$ is a graph with edge ideal $I(G)$. For every integer $s\geq 1$, we denote the squarefree part of the $s$-th symbolic power of $I(G)$ by $I(G)^{\{s\}}$. We determine an upper bound for the regularity of $I(G)^{\{s\}}$ when $G$ is a cho
Externí odkaz:
http://arxiv.org/abs/2303.02791
Autor:
Fakhari, S. A. Seyed
Assume that $G$ is a graph with edge ideal $I(G)$ and matching number ${\rm match}(G)$. For every integer $s\geq 1$, we denote the $s$-th squarefree power of $I(G)$ by $I(G)^{[s]}$. It is shown that for every positive integer $s\leq {\rm match}(G)$,
Externí odkaz:
http://arxiv.org/abs/2207.08559
Autor:
Fakhari, S. A. Seyed
Assume that $G$ is a graph with edge ideal $I(G)$. We provide sharp lower bounds for the depth of $I(G)^2$ in terms of the star packing number of $G$.
Externí odkaz:
http://arxiv.org/abs/2202.12661
Autor:
Fakhari, S. A. Seyed
For any graph $G$, assume that $J(G)$ is the cover ideal of $G$. Let $J(G)^{(k)}$ denote the $k$th symbolic power of $J(G)$. We characterize all graphs $G$ with the property that $J(G)^{(k)}$ has a linear resolution for some (equivalently, for all) i
Externí odkaz:
http://arxiv.org/abs/2010.08878
Autor:
Fakhari, S. A. Seyed
Assume that $G$ is a graph with edge ideal $I(G)$ and star packing number $\alpha_2(G)$. We denote the $s$-th symbolic power of $I(G)$ by $I(G)^{(s)}$. It is shown that the inequality ${\rm depth} S/(I(G)^{(s)})\geq \alpha_2(G)-s+1$ is true for every
Externí odkaz:
http://arxiv.org/abs/2004.05037
Autor:
Fakhari, S. A. Seyed
Assume that $G$ is a graph with edge ideal $I(G)$ and let $I(G)^{(s)}$ denote the $s$-th symbolic power of $I(G)$. It is proved that for every integer $s\geq 1$, $${\rm reg}(I(G)^{(s+1)})\leq \max\bigg\{{\rm reg}(I(G))+2s, {\rm reg}\big(I(G)^{(s+1)}+
Externí odkaz:
http://arxiv.org/abs/1908.10845