Results 41 to 50 of about 237,348 (199)
Free Resolutions and Generalized Hamming Weights of Binary Linear Codes
Mathematics, 2022 In this work, we explore the relationship between the graded free resolution of some monomial ideals and the Generalized Hamming Weights (GHWs) of binary codes.
Ignacio García-Marco +3 more
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Divisors on graphs, Connected flags, and Syzygies [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We study the binomial and monomial ideals arising from linear equivalence of divisors on graphs from the point of view of Gröbner theory. We give an explicit description of a minimal Gröbner basis for each higher syzygy module.
Fatemeh Mohammadi, Farbod Shokrieh
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A remark on sequentially Cohen-Macaulay monomial ideals [PDF]
Transactions on CombinatoricsLet $R=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. We show that if $G$ is a connected graph with a basic $5$-cycle $C$, then $G$ is a sequentially Cohen-Macaulay graph if and only if there exists a shedding vertex $x$ of $
Mozhgan Koolani, Amir Mafi
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Current Trends on Monomial and Binomial Ideals [PDF]
, 2020 Historically, the study of monomial ideals became fashionable after the pioneering work by Richard Stanley in 1975 on the upper bound conjecture for spheres.
Hibi, Takayuki, H
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Algebraic Properties of Monomial Ideals
, 2015 In this thesis we first study a special class of squarefree monomial ideals, namely, path ideals. We give a formula to compute all graded Betti numbers of the path ideal of a cycle and a path.
Alilooee, Ali
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Monomial ideals via square-free monomial ideals [PDF]
, 2005 Corrected Statement of Corollary 2.6 (took one statement out)
openaire +3 more sources
A note on minimal resolutions of vector–spread Borel ideals
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 We consider vector–spread Borel ideals. We show that these ideals have linear quotients and thereby we determine the graded Betti numbers and the bigraded Poincaré series.
Crupi Marilena, Ficarra Antonino
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Algebraic Analysis of Variants of Multi-State k-out-of-n Systems
Mathematics, 2021 We apply the algebraic reliability method to the analysis of several variants of multi-state k-out-of-n systems. We describe and use the reliability ideals of multi-state consecutive k-out-of-n systems with and without sparse, and show the results of ...
Patricia Pascual-Ortigosa +1 more
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Cohen–Macaulayness of Vertex Splittable Monomial Ideals
MathematicsIn this paper, we give a new criterion for the Cohen–Macaulayness of vertex splittable ideals, a family of monomial ideals recently introduced by Moradi and Khosh-Ahang. Our result relies on a Betti splitting of the ideal and provides an inductive way of
Marilena Crupi, Antonino Ficarra
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When Is a Graded Free Complex Exact?
Mathematics, 2022 Minimal free resolutions of a finitely generated module over a polynomial ring S=k[x], with variables x={x1,…,xn} and a field k have been extensively studied.
David C. Molano +2 more
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