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pro vyhledávání: '"Veer, Dharm"'
In this article, we characterize Cohen-Macaulay permutation graphs. In particular, we show that a permutation graph is Cohen-Macaulay if and only if it is well-covered and there exists a unique way of partitioning its vertex set into $r$ disjoint max
Externí odkaz:
http://arxiv.org/abs/2310.17343
Autor:
Veer, Dharm
In this article, we prove that if a Hibi ring satisfies property $N_2$, then its Segre product with a polynomial ring in finitely many variables also satisfies property $N_2$. When the polynomial ring is in two variables, we also prove the above stat
Externí odkaz:
http://arxiv.org/abs/2305.05659
Autor:
Jahangir, Rizwan, Veer, Dharm
We characterize Cohen-Macaulay posets of dimension two; they are precisely the shellable and strongly connected posets of dimension two. We also give a combinatorial description of these posets. Using the fact that co-comparability graph of a 2-dimen
Externí odkaz:
http://arxiv.org/abs/2305.04535
In this article, we study the primary decomposition of some binomial ideals. In particular, we introduce the concept of polyocollection, a combinatorial object that generalizes the definitions of collection of cells and polyomino, that can be used to
Externí odkaz:
http://arxiv.org/abs/2302.08337
Autor:
Kummini, Manoj, Veer, Dharm
Let $\mathcal{P}$ be a simple thin polyomino and $\Bbbk$ a field. Let $R$ be the toric $\Bbbk$-algebra associated to $\mathcal{P}$. Write the Hilbert series of $R$ as $h_{R}(t)/(1-t)^{\dim(R)}$. We show that $$(-1)^{\left\lfloor{\frac{\mathrm{deg} h_
Externí odkaz:
http://arxiv.org/abs/2203.03487
Autor:
Kummini, Manoj, Veer, Dharm
Let $X$ be a convex polyomino such that its vertex set is a sublattice of $\mathbb{N}^2$. Let $\Bbbk[X]$ be the toric ring (over a field $\Bbbk$) associated to $X$ in the sense of Qureshi, \emph{J. Algebra}, 2012. Write the Hilbert series of $\Bbbk[X
Externí odkaz:
http://arxiv.org/abs/2110.14905
Autor:
Veer, Dharm
In this article, we prove necessary conditions for Hibi rings to satisfy Green-Lazarsfeld property $N_p$ for $p=2$ and $3$. We also show that if a Hibi ring satisfies property $N_4$, then it is a polynomial ring or it has a linear resolution. Therefo
Externí odkaz:
http://arxiv.org/abs/2108.03915
Publikováno v:
In Journal of Algebra 1 March 2024 641:498-529
Publikováno v:
In Materials Letters: X June 2023 18
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