Results 11 to 20 of about 2,508,330 (246)

Depth, Stanley depth and regularity of ideals associated to graphs

Archiv der Mathematik, 2016
Let $\mathbb{K}$ be a field and $S=\mathbb{K}[x_1,\dots,x_n]$ be the polynomial ring in $n$ variables over $\mathbb{K}$. Let $G$ be a graph with $n$ vertices. Assume that $I=I(G)$ is the edge ideal of $G$ and $J=J(G)$ is its cover ideal. We prove that ${\
Fakhari, S. A. Seyed
core   +6 more sources

Stanley depth of squarefree Veronese ideals [PDF]

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013
We compute the Stanley depth for the quotient ring of a square free Veronese ideal and we give some bounds for the Stanley depth of a square free Veronese ideal. In particular, it follows that both satisfy the Stanley's conjecture.
Cimpoeas Mircea
doaj   +3 more sources

Stanley depth and the lcm-lattice [PDF]

Journal of Combinatorial Theory, Series A, 2017
In this paper we show that the Stanley depth, as well as the usual depth, are essentially determined by the lcm-lattice. More precisely, we show that for quotients $I/J$ of monomial ideals $J\subset I$, both invariants behave monotonic with respect to ...
Ichim, Bogdan, Katthän, Lukas, Moyano-Fernández, Julio José   +2 more
core   +5 more sources

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

Betti posets and the Stanley depth [PDF]

Arnold Mathematical Journal, 2015
Let S be a polynomial ring and let I ⊆ S be a monomial ideal. In this short note, we propose the conjecture that the Betti poset of I determines the Stanley projective dimension of S/I or I .
Lukas Katthan
semanticscholar   +4 more sources

The behavior of Stanley depth under polarization [PDF]

Journal of Combinatorial Theory, Series A, 2014
Let $K$ be a field, $R=K[X_1, ..., X_n]$ be the polynomial ring and $J \subsetneq I$ two monomial ideals in $R$. In this paper we show that $\mathrm{sdepth}\ {I/J} - \mathrm{depth}\ {I/J} = \mathrm{sdepth}\ {I^p/J^p}-\mathrm{depth}\ {I^p/J^p}$, where ...
Bogdan Ichim, José Moyano-fernández, Julio, Lukas Katthän   +3 more
core   +5 more sources

On the Stanley Depth of Squarefree Veronese Ideals [PDF]

Journal of Algebraic Combinatorics, 2009
Let $K$ be a field and $S=K[x_1,...,x_n]$. In 1982, Stanley defined what is now called the Stanley depth of an $S$-module $M$, denoted $\sdepth(M)$, and conjectured that $\depth(M) \le \sdepth(M)$ for all finitely generated $S$-modules $M$.
J. Young, Mitchel T. Keller, Noah Streib, Stephen, Yi-huang Shen   +4 more
core   +5 more sources

A Variant of the Stanley Depth for Multisets [PDF]

Discrete Mathematics, 2019
We define and study a variant of the \emph{Stanley depth} which we call \emph{total depth} for partially ordered sets (posets). This total depth is the most natural variant of Stanley depth from $\llbracket S_k\rrbracket$ -- the poset of nonempty subsets
Wang, Yinghui
core   +2 more sources

Stanley depth of quotient of monomial complete intersection ideals [PDF]

Communications in Algebra, 2013
We compute the Stanley depth for a particular, but important case, of the quotient of complete intersection monomial ideals. Also, in the general case, we give sharp bounds for the Stanley depth of a quotient of complete intersection monomial ideals.
Cimpoeas, Mircea
core   +2 more sources

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
doaj   +3 more sources