Results 41 to 50 of about 14,720 (185)
Generic initial ideals of modular polynomial invariants
, 2020 We study the generic initial ideals (gin) of certain ideals that arise in modular invariant theory. For all cases an explicit generating set is known we calculate the generic initial ideal of the Hilbert ideal of a cyclic group of prime order for all ...
Danış, Bekir, Sezer, Müfit
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Generic Cohen-Macaulay Monomial Ideals [PDF]
Annals of Combinatorics, 2004 18 pages, 8 ...
Jarrah, Abdul Salam +1 more
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Monomial ideals of minimal depth
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013 Let S be a polynomial algebra over a field. We study classes of monomial ideals (as for example lexsegment ideals) of S having minimal depth. In particular, Stanley's conjecture holds for these ideals.
Ishaq Muhammad
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Symbolic Powers of Monomial Ideals [PDF]
Proceedings of the Edinburgh Mathematical Society, 2016 AbstractWe investigate symbolic and regular powers of monomial ideals. For a square-free monomial ideal I ⊆ 𝕜[x0, … , xn] we show that for all positive integers m, t and r, where e is the big-height of I and . This captures two conjectures (r = 1 and r = e): one of Harbourne and Huneke, and one of Bocci et al. We also introduce the symbolic polyhedron
Cooper, Susan M. +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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Multiplicities of monomial ideals
Journal of Algebra, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Herzog, Jürgen, Srinivasan, Hema
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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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Integer sequences and monomial ideals
Proceedings - Mathematical Sciences, 2021 Let $\mathfrak{S}_n$ be the set of all permutations of $[n]=\{1,\ldots,n\}$ and let $W$ be the subset consisting of permutations $σ\in \mathfrak{S}_n$ avoiding 132 and 312-patterns. The monomial ideal $I_W = \left\langle \mathbf{x}^σ = \prod_{i=1}^n x_i^{σ(i)} : σ\in W \right\rangle $ in the polynomial ring $R = k[x_1,\ldots,x_n]$ over a field $k$ is ...
Kumar, Chanchal, Roy, Amit
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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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Degenerations of Monomial Ideals [PDF]
Mathematical Research Letters, 2004 In the paper under review the author describes the degenerations of monomial ideals in \(K[[x,y]]\) with \(\text{ Aut}(K[[x,y]])\)-orbit of dimension at most \(3\). In particular, she determines the monomial ideals that any power of \((x,y^4)\) can degenerate to and makes a conjecture about all the ideals that the powers of \((x,y^4)\) can degenerate ...
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