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On Characteristic Poset and Stanley Decomposition [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 Let J ⊂ I be two monomial ideals such that I/J is Cohen Macaulay. By associating a finite posets PI/Jg$P_{I/J}^g$ to I/J, we show that if I/J is a Stanley ideal then I/J˜$\widetilde{I/J}$ is also a Stanley ideal, where I/J˜$\widetilde{I/J}$ is the ...
Ahmad Sarfraz +2 more
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Stanley–Reisner rings and the occurrence of the Steinberg representation in the hit problem [PDF]
Comptes Rendus. Mathématique, 2022 A result of G. Walker and R. Wood states that the space of indecomposable elements in degree $2^n-1-n$ of the polynomial algebra $\mathbb{F}_2[x_1,\,\ldots ,\,x_n]$, considered as a module over the mod 2 Steenrod algebra, is isomorphic to the Steinberg ...
Hai, Nguyen Dang Ho
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Graded Linearity of Stanley–Reisner Ring of Broken Circuit Complexes [PDF]
Journal of Mathematics, 2022 This paper introduces two new notions of graded linear resolution and graded linear quotients, which generalize the concepts of linear resolution property and linear quotient for modules over the polynomial ring A=kx1,…,xn.
Mohammad Reza-Rahmati, Gerardo Flores
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Fuzzy backstepping controller for agricultural tractor-trailer vehicles path tracking control with experimental validation [PDF]
Frontiers in Plant ScienceUnmanned driving technology for agricultural vehicles is pivotal in advancing modern agriculture towards precision, intelligence, and sustainability. Among agricultural machinery, autonomous driving technology for agricultural tractor-trailer vehicles ...
Anzhe Wang +9 more
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Stanley decompositions and Hilbert depth in the Koszul complex
Journal of Commutative Algebra, 2010 Stanley decompositions of multigraded modules $M$ over polynomials rings have been discussed intensively in recent years. There is a natural notion of depth that goes with a Stanley decomposition, called the Stanley depth.
Bruns, Winfried +2 more
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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 +2 more
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Block Stanley decompositions I. Elementary and gnomon decompositions [PDF]
Journal of Pure and Applied Algebra, 2015 Stanley decompositions are used in invariant theory and the theory of normal forms for dynamical systems to provide a unique way of writing each invariant as a polynomial in the Hilbert basis elements. Since the required Stanley decompositions can be very long, we introduce a more concise notation called a block decomposition, along with three notions ...
Murdock, James, Murdock, Theodore
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Structure and enumeration of $(3+1)$-free posets (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 A poset is $(3+1)$-free if it does not contain the disjoint union of chains of length 3 and 1 as an induced subposet. These posets are the subject of the $(3+1)$-free conjecture of Stanley and Stembridge.
Mathieu Guay-Paquet +2 more
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Stanley decompositions in localized polynomial rings [PDF]
Manuscripta Mathematica, 2010 12 pages, 2 ...
Nasir, Sumiya, Rauf, Asia
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Stanley decompositions and partitionable simplicial complexes [PDF]
Journal of Algebraic Combinatorics, 2007 We study Stanley decompositions and show that Stanley's conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.
Herzog, Jürgen +2 more
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