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Let $I(G)^{[k]}$ denote the $k^{th}$ square-free power of the edge ideal $I(G)$ of a graph $G$. In this article, we provide a precise formula for the depth of $I(G)^{[k]}$ when $G$ is a Cohen-Macaulay forest. Using this, we show that for a Cohen-Maca
Externí odkaz:
http://arxiv.org/abs/2409.06021
Autor:
Bhardwaj, Om Prakash, Saha, Kamalesh
Some recent investigations indicate that for the classification of Cohen-Macaulay binomial edge ideals, it suffices to consider biconnected graphs with some whiskers attached (in short, `block with whiskers'). This paper provides explicit combinatori
Externí odkaz:
http://arxiv.org/abs/2409.01639
Hand gestures have evolved into a natural and intuitive means of engaging with technology. The objective of this research is to develop a robust system that can accurately recognize and classify hand gestures representing numbers. The proposed approa
Externí odkaz:
http://arxiv.org/abs/2407.10902
Autor:
Saha, Kamalesh
Let $I\subset A$ and $J\subset B$ be two monomial ideals, where $A$ and $B$ are two polynomial rings with disjoint variables. Considering a general set-up of monomial filtrations, we study the behaviour of the $\mathrm{v}$-function under binomial exp
Externí odkaz:
http://arxiv.org/abs/2406.05567
In this article, we give combinatorial formulas for the regularity and the projective dimension of $3$-path ideals of chordal graphs, extending the well-known formulas for the edge ideals of chordal graphs given in terms of the induced matching numbe
Externí odkaz:
http://arxiv.org/abs/2405.15897
Let $G$ be a finite simple graph, and $J_G$ denote the binomial edge ideal of $G$. In this article, we first compute the $\mathrm{v}$-number of binomial edge ideals corresponding to Cohen-Macaulay closed graphs. As a consequence, we obtain the $\math
Externí odkaz:
http://arxiv.org/abs/2405.15354
In this paper, we study the asymptotic behaviour of the v-number of a Noetherian graded filtration $\mathcal{I}= \{I_{[k]}\}_{k\geq 0}$ of a Noetherian $\mathbb{N}$-graded domain $R$. Recently, it is shown that $\mathrm{v}(I_{[k]})$ is periodically l
Externí odkaz:
http://arxiv.org/abs/2404.00493
Our theoretical study unfolds the topological phase transitions (within bands of the Moir\'e super-lattice) in small angle twisted double bilayer graphene (tDBLG) under the influence of external gate voltage and intrinsic spin-orbit coupling (SOC) fo
Externí odkaz:
http://arxiv.org/abs/2403.11660
Recently, Ficarra and Sgroi initiated the study of v-numbers of powers of graded ideals. They proved that for a graded ideal $I$ in a polynomial ring $S$, $\mathrm{v}(I^k)$ is a linear function in $k$ for $k>>0$. Later, Ficarra conjectured that if $I
Externí odkaz:
http://arxiv.org/abs/2402.16583
This research focuses on analyzing the depth of generalized binomial edge ideals. We extend the notion of $d$-compatible map for the pairs of a complete graph and an arbitrary graph, and using it, we give a combinatorial lower bound for the depth of
Externí odkaz:
http://arxiv.org/abs/2401.06573