Results 101 to 110 of about 14,720 (185)
Trees, parking functions, syzygies, and deformations of monomial ideals
, 2003 For a graph G, we construct two algebras, whose dimensions are both equal to the number of spanning trees of G. One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ...
Postnikov, Alexander, Shapiro, Boris
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ON THE STANLEY DEPTH OF EDGE IDEALS OF LINE AND CYCLIC GRAPHS
Romanian Journal of Mathematics and Computer Science, 2015 We prove that the edge ideals of line and cyclic graphs and their quotient rings satisfy the Stanley conjecture. We compute the Stanley depth for the quotient ring of the edge ideal associated to a cycle graph of length n, given a precise formula for n ≡
MIRCEA CIMPOEAS
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Illinois Journal of Mathematics, 2007 A Gotzmann monomial ideal of the polynomial ring is a monomial ideal which is generated in one degree and which satisfies Gotzmann's persistence theorem. A subset $V$ is said to be a Gotzmann subset if the ideal generated by $V$ is a Gotzmann monomial ideal.
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On the weak Lefschetz property of graded modules over K[x, y]
Le Matematiche, 2012 It is known that graded cyclic modules over S = K[x, y] have the Weak Lefschetz Property (WLP). This is not true for non-cyclic modules over S. The purpose of this note is to study which conditions on S-modules ensure the WLP.
Giuseppe Favacchio, Phong Dinh Thieu
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Stanley's conjecture, cover depth and extremal simplicial complexes
Le Matematiche, 2008 A famous conjecture by R. Stanley relates the depth of a module, an algebraic invariant, with the so-called Stanley depth, a geometric one. We describe two related geometric notions, the cover depth and the greedy depth, and we study their relations with
Benjamin Nill, Kathrin Vorwerk
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Border Basis of an Ideal of Points and its Application in Experimental Design and Regression
پژوهشهای ریاضی, 2020 Introduction Border bases are a generalization of Gröbner bases for zero-dimensional ideals which have attracted the interest of many researchers recently. More precisely, border bases provide a new method to find a structurally stable monomial basis for
Samira Poukhajouei +2 more
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Illinois Journal of Mathematics, 2004 Generalizing a construction of \textit{A. V. Geramita}, \textit{T. Harima} and \textit{Y. S. Shin} [Ill. J. Math 45, 1--23 (2001; Zbl 1095.13500)], the author introduces so-called \(n\)-lists: A \(1\)-list is a natural number, and for \(n\geq 1\) an \(n\)-list is a decreasing infinite sequence of \((n- 1)\)-lists, where \(A\geq B\) for two \(n\)-lists \
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Local Cohomology at Monomial Ideals
Journal of Symbolic Computation, 2000 For a reduced monomial ideal B in R=k[X_1,...,X_n], we write H^i_B(R) as the union of {Ext^i(R/B^[d],R)}_d, where {B^[d]}_d are the "Frobenius powers of B". We describe H^i_B(R)_p, for every p in Z^n, in the spirit of the Stanley-Reisner theory. As a first application we give an isomorphism Tor_i(B', k)_p\iso Ext^{|p|-i}(R/B,R)_{-p} for all p in {0,1 ...
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Tameness of local cohomology of monomial ideals with respect to monomial prime ideals
Journal of Pure and Applied Algebra, 2007 In this paper we consider the local cohomology of monomial ideals with respect to monomial prime ideals and show that all these local cohomology modules are tame.
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, 2008 In analogy to the skeletons of a simplicial complex and their Stanley--Reisner ideals we introduce the skeletons of an arbitrary monomial ideal $I\subset S=K[x_1,...,x_n]$. This allows us to compute the depth of $S/I$ in terms of its skeleton ideals. We apply these techniques to show that Stanley's conjecture on Stanley decompositions of $S/I$ holds ...
Herzog, Juergen +2 more
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