Zobrazeno 1 - 10
of 248
pro vyhledávání: '"Sáenz de Cabezón A"'
Autor:
Kling, Filip Jonsson, Lundqvist, Samuel, Mohammadi, Fatemeh, Orth, Matthias, Sáenz-de-Cabezón, Eduardo
For the almost complete intersection ideals $(x_1^2, \dots, x_n^2, (x_1 + \cdots + x_n)^k)$, we compute their reduced Gr\"obner basis for any term ordering, revealing a combinatorial structure linked to lattice paths, elementary symmetric polynomials
Externí odkaz:
http://arxiv.org/abs/2411.10209
Autor:
Iglesias, Rodrigo, Mohammadi, Fatemeh, Pascual-Ortigosa, Patricia, Sáenz-de-Cabezón, Eduardo, Wynn, Henry P.
Publikováno v:
Applicable Algebra in Engineering, Communication and Computing 2024
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of stable systems
Externí odkaz:
http://arxiv.org/abs/2406.00829
We prove that the Pommaret-Seiler resolution for quasi-stable ideals is cellular and give a cellular structure for it. This shows that this resolution is a generalization of the well known Eliahou-Kervaire resolution for stable ideals in a deeper sen
Externí odkaz:
http://arxiv.org/abs/2401.13788
Let $I$ be a monomial ideal in two variables generated by three monomials and let $\mathcal{R}(I)$ be its Rees ideal. We describe an algorithm to compute the minimal generating set of $\mathcal{R}(I)$. Based on the data obtained by this algorithm, we
Externí odkaz:
http://arxiv.org/abs/2401.11558
Autor:
González-Sarabia, Manuel, Muñoz-George, Humberto, Ordaz, Jorge A., Sáenz-de-Cabezón, Eduardo, Villarreal, Rafael H.
For projective Reed--Muller-type codes we give a global duality criterion in terms of the v-number and the Hilbert function of a vanishing ideal. As an application, we provide a global duality theorem for projective Reed--Muller-type codes over Goren
Externí odkaz:
http://arxiv.org/abs/2308.13728
We present the design and implementation of a \texttt{C++} class for reliability analysis of multi-state systems using an algebraic approach based on monomial ideals. The class is implemented within the open-source \verb|CoCoALib| library and provide
Externí odkaz:
http://arxiv.org/abs/2109.08458
The support poset of a monomial ideal $I\subseteq\mathbf{k}[x_1,\dots,x_n]$ encodes the relation between the variables $x_1,\dots,x_n$ and the minimal monomial generators of $I$. It is known that not every poset is realizable as the support poset of
Externí odkaz:
http://arxiv.org/abs/2009.08125
In this paper we review different definitions that multi-state $k$-out-of-$n$ systems have received along the literature and study them in a unified way using the algebra of monomial ideals. We thus obtain formulas and algorithms to compute their rel
Externí odkaz:
http://arxiv.org/abs/2002.08823
Polarization and depolarization of monomial ideals with application to multistate system reliability
Publikováno v:
Journal of Algebraic Combinatorics (2019)
We study the family of depolarizations of a squarefree monomial ideal $I$, i.e. all monomial ideals whose polarization is $I$. We describe a method to find all depolarizations of $I$ and study some of the properties they share and some they do not sh
Externí odkaz:
http://arxiv.org/abs/1807.05743
We study multiple simultaneous cut events for k-out-of-n:F and linear consecutive k-out-of-n:F systems in which each component has a constant failure probability. We list the multicuts of these systems and describe the structural differences between
Externí odkaz:
http://arxiv.org/abs/1712.08042