Results 21 to 30 of about 2,508,330 (246)
Depth and Stanley depth of the path ideal associated to an $n$-cyclic graph [PDF]
TURKISH JOURNAL OF MATHEMATICS, 2016 We compute the depth and Stanley depth for the quotient ring of the path ideal of length $3$ associated to a $n$-cyclic graph, given some precise formulas for depth when $n\not\equiv 1\,(\mbox{mod}\ 4)$, tight bounds when $n\equiv 1\,(\mbox{mod}\ 4)$ and
G. Zhu
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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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A non-partitionable Cohen–Macaulay simplicial complex [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A long-standing conjecture of Stanley states that every Cohen–Macaulay simplicial complex is partition- able. We disprove the conjecture by constructing an explicit counterexample.
Art M. Duval +3 more
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Some algebraic invariants of the edge ideals of perfect [h,d]-ary trees and some unicyclic graphs
AIMS Mathematics, 2023 This article is mainly concerned with computations of some algebraic invariants of quotient rings of edge ideals of perfect [h,d]-ary trees and unicyclic graphs. We compute exact values of depth and Stanley depth and consequently projective dimension for
Tazeen Ayesha, Muhammad Ishaq
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TRANSFER OF HEAVY METALS IN SOIL IN-PLUM CULTIVATION: A FIELD STUDY IN ADAMACHI IASI, ROMANIA [PDF]
Journal of Applied Life Sciences and Environment, 2023 Currently, global environmental concerns about heavy metal pollution are driven by rapid urbanization and industrial development. Therefore, a field study was conducted to assess the concentration of heavy metals (Pb, Co, Zn, Ni and Cu) in orchard soils ...
Mariana RUSU +5 more
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Depth and Stanley depth of the edge ideals of the strong product of some graphs [PDF]
Hacettepe Journal of Mathematics and Statistics, 2019 In this paper we study depth and Stanley depth of the edge ideals and quotient rings of the edge ideals, associated to classes of graphs obtained by taking the strong product of two graphs.
Zahid Iqbal, M. Ishaq, M. Binyamin
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Stanley depth of weakly polymatroidal ideals [PDF]
Archiv der Mathematik, 2014 Let $\mathbb{K}$ be a field and $S=\mathbb{K}[x_1,\dots,x_n]$ be the polynomial ring in $n$ variables over the field $\mathbb{K}$. In this paper, it is shown that Stanley's conjecture holds for $S/I$, if $I$ is a weakly polymatroidal ideal.
Pournaki, M. +2 more
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Stanley depth of edge ideals [PDF]
Studia Scientiarum Mathematicarum Hungarica, 2012 We give an upper bound for the Stanley depth of the edge idealIof ak-partite complete graph and show that Stanley’s conjecture holds forI. Also we give an upper bound for the Stanley depth of the edge ideal of as-uniform complete bipartite hypergraph.
Ishaq, Muhammad, Qureshi, Muhammad Imran
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Combinatorial Reductions for the Stanley Depth of $I$ and $S/I$ [PDF]
Electronic Journal of Combinatorics, 2017 We develop combinatorial tools to study the relationship between the Stanley depth of a monomial ideal $I$ and the Stanley depth of its compliment, $S/I$.
Mitchel T. Keller, Stephen J. Young
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