Results 61 to 70 of about 1,836,425 (146)

Zafar: Algebraic properties of the binomial edge ideal of complete bipartite graph

, 2020
Let JG denote the binomial edge ideal of a connected undirected graph on n vertices. This is the ideal generated by the binomials xiyj − xjyi, 1 ≤ i < j ≤ n, in the polynomial ring S = K[x1, . . . , xn, y1, . . . , yn] where {i, j} is an edge of G. We
Peter Schenzel, Sohail Zafar
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Semantical and Grammatical Peculiarities of Binomial Expressions in English [PDF]

, 2011
Binomial expressions are a sequence of two or more words or phrases, which consist of elements belonging to the same category. They may be connected by a coordinating conjunction or a preposition.
Котнюк Л. Г.
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Generalized Binomial Trees [PDF]

We consider the problem of consistently pricing new options given the prices of related options on the same stock. The Black-Scholes formula and standard binomial trees can only accommodate one related European option which then effectively specifies the
Jackwerth, Jens Carsten
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Arithmetical rank of binomial ideals [PDF]

, 2017
In this paper, we investigate the arithmetical rank of a binomial ideal J. We provide lower bounds for the binomial arithmetical rank and the J-complete arithmetical rank of J. Special attention is paid to the case where J is the binomial edge ideal of a
Anargyros Katsabekis, Katsabekis, A.
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The $\mathrm{v}$-Number of Binomial Edge Ideals [PDF]

, 2023
The invariant $\mathrm{v}$-number was introduced very recently in the study of Reed-Muller-type codes. Jaramillo and Villarreal (J Combin. Theory Ser. A 177:105310, 2021) initiated the study of the $\mathrm{v}$-number of edge ideals.
Sengupta, Indranath, Ambhore, Siddhi Balu, Saha, Kamalesh   +2 more
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Partial Betti splittings with applications to binomial edge ideals

We introduce the notion of a partial Betti splitting of a homogeneous ideal, generalizing the notion of a Betti splitting first given by Francisco, Hà, and Van Tuyl.
Sivakumar, Aniketh, Van Tuyl, Adam, Jayanthan, A. V.   +2 more
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Generalized binomial edge ideals of complete $r$-partite graphs

, 2023
This paper analyzes the cohomological dimension of the generalized binomial edge ideal $\calJ_{K_m,G}$ for a complete $r$-partite graph $G$. Additionally, the Krull dimension, the depth, the Castelnuovo--Mumford regularity, the Hilbert series, and the ...
Shen, Yi-Huang, Zhu, Guangjun
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On the $\mathrm{v}$-number of binomial edge ideals of some classes of graphs [PDF]

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 $\mathrm{v}
Dey, Deblina, Jayanthan, A. V., Saha, Kamalesh   +2 more
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Generalized binomial edge ideals of bipartite graphs

, 2023
Connected bipartite graphs whose binomial edge ideals are Cohen--Macaulay have been classified by Bolognini et al. In this paper, we compute the depth, Castelnuovo--Mumford regularity, and dimension of the generalized binomial edge ideals of these ...
Shen, Yi-Huang, Zhu, Guangjun
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Some vanishing sums involving binomial coefficients in the denominator [PDF]

, 2008
Identities involving binomial coeffcients usually arise in situations where counting is carried out in two different ways. For instance, some identities obtained by William Horrace [1] using probability theory turn out to be special cases of the Chu ...
Sury, B., Purkait, S. (Soma)
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