Results 1 to 10 of about 25,354 (185)

Monomial ideals under ideal operations [PDF]

Communications in Algebra, 2013
In this paper, we show for a monomial ideal $I$ of $K[x_1,x_2,\ldots,x_n]$ that the integral closure $\ol{I}$ is a monomial ideal of Borel type (Borel-fixed, strongly stable, lexsegment, or universal lexsegment respectively), if $I$ has the same property.
Guo, Jin, Wu, Tongsuo
core   +3 more sources

Stanley depth of monomial ideals with small number of generators

Open Mathematics, 2009
For a monomial ideal $I\subset S=K[x_1,...,x_n]$, we show that $\sdepth(S/I)\geq n-g(I)$, where $g(I)$ is the number of the minimal monomial generators of $I$. If $I=vI'$, where $v\in S$ is a monomial, then we see that $\sdepth(S/I)=\sdepth(S/I')$.
Cimpoeaş Mircea
doaj   +2 more sources

Symbolic Powers of Monomial Ideals [PDF]

Proceedings of the Edinburgh Mathematical Society, 2016
We investigate symbolic and regular powers of monomial ideals. For a square-free monomial ideal $I$ in $k[x_0, \ldots, x_n]$ we show $I^{t(m+e-1)-e+r)}$ is a subset of $M^{(t-1)(e-1)+r-1}(I^{(m)})^t$ for all positive integers $m$, $t$ and $r$, where $e ...
Cooper, Susan M., Embree, Robert J. D., Hoefel, Andrew H., Hà, Huy Tài   +3 more
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Algebraic invariants of the edge ideals of whisker graphs of cubic circulant graphs [PDF]

Heliyon
Let Q be a polynomial ring over a field F and I be an edge ideal associated with the whisker graph of a cubic circulant graph. We discuss the regularity, depth, Stanley depth, and projective dimension of Q/I.
Mujahid Ullah Khan Afridi, Ibad Ur Rehman, Muhammad Ishaq   +2 more
doaj   +2 more sources

Regularity of the edge ideals of perfect [ν,h]-ary trees and some unicyclic graphs [PDF]

Heliyon
We compute the Castelnuovo-Mumford regularity of the quotient rings of edge ideals of perfect [ν,h]-ary trees and some unicyclic graphs.
Fatima Tul Zahra, Muhammad Ishaq, Sarah Aljohani   +2 more
doaj   +2 more sources

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, Bennet Goeckner, Caroline J. Klivans, Jeremy Martin   +3 more
doaj   +1 more source

Values and bounds for depth and Stanley depth of some classes of edge ideals

AIMS Mathematics, 2021
In this paper we study depth and Stanley depth of the quotient rings of the edge ideals associated with the corona product of some classes of graphs with arbitrary non-trivial connected graph G.
Naeem Ud Din, Muhammad Ishaq, Zunaira Sajid   +2 more
doaj   +1 more source

Bounds for the minimum distance function

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
Let I be a homogeneous ideal in a polynomial ring S. In this paper, we extend the study of the asymptotic behavior of the minimum distance function δI of I and give bounds for its stabilization point, rI, when I is an F -pure or a square-free monomial ...
Núñez-Betancourt Luis, Pitones Yuriko, Villarreal Rafael H.   +2 more
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Study and characterization of some classes of polymatroidal ideals

پژوهش‌های ریاضی, 2022
Introduction Throughout this paper, we consider monomial ideals of the polynomial ring  over a filed. We try to give some properties of the polymatroidal ideals, which are the special class of monomial ideals.
Somayeh Bandari
doaj  

Monomial s-sequences arising from graph ideals

Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2023
Ideals arising from graphs are investigated via s-sequence theory. In particular, the notion of s-sequence for the generators of the edge ideal I(G) of an acyclic graph G is considered for describing the Groebner basis of the relation ideal J of the ...
Maurizio Imbesi, Monica La Barbiera
doaj   +1 more source