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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 decomposition of the joint covariants of three quadratics [PDF]
Regular and Chaotic Dynamics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jan A Sanders
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The Stanley decomposition of the harmonic oscillator
Proceedings of the Koninklijke Nederlandse Akademie Van Wetenschappen Series A, Indagationes Mathematicae, 1988 The authors derive a new decomposition of the ring of polynomial functions on the variety of \((n+1)\times (n+1)\) complex matrices of rank less than or equal to 1. This involves the Stanley decomposition [cf. \textit{R. P. Stanley}, Invent. Math. 68, 175-193 (1982; Zbl 0516.10009)] of the monoid \(\{(i,j)\in {\mathbb{N}}^{n+1}\times {\mathbb{N}}^{n+1}:
Billera, L.J. +2 more
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Stanley Decomposition for Coupled Takens–Bogdanov Systems
Journal of Nonlinear Mathematical Physics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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.
Siamak Yassemi, Jürgen Herzog
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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–Reisner rings and the occurrence of the Steinberg representation in the hit problem
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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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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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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Graded Linearity of Stanley–Reisner Ring of Broken Circuit Complexes
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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