Results 21 to 30 of about 520,160 (245)
Stanley’s conjecture for critical ideals [PDF]
Studia Scientiarum Mathematicarum Hungarica, 2011 Let S = K[x1,…,xn] be a polynomial ring in n variables over a field K. Stanley’s conjecture holds for the modules I and S/I, when I ⊂ S is a critical monomial ideal. We calculate the Stanley depth of S/I when I is a canonical critical monomial ideal.
Haider, Azeem, Khan, Sardar Mohib Ali
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A Conjecture of Stanley on Alternating Permutations [PDF]
The Electronic Journal of Combinatorics, 2007 We give two simple proofs of a conjecture of Richard Stanley concerning the equidistribution of derangements and alternating permutations with the maximal number of fixed points.
Chapman, Robin, Williams, Lauren K.
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AIMS Mathematics, 2022 In this paper, we study depth and Stanley depth of the quotient rings of the edge ideals associated to triangular and multi triangular snake and triangular and multi triangular ouroboros snake graphs.
Malik Muhammad Suleman Shahid +3 more
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Stanley's zrank conjecture on skew partitions [PDF]
Transactions of the American Mathematical Society, 2008 Summary: We present an affirmative answer to Stanley's zrank conjecture, namely, the zrank and the rank are equal for any skew partition. We show that certain classes of restricted Cauchy matrices are nonsingular and furthermore, the signs are determined by the number of zero entries.
Chen, William Y. C., Yang, Arthur L. B.
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Balanced labellings of affine permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We study the $\textit{diagrams}$ of affine permutations and their $\textit{balanced}$ labellings. As in the finite case, which was investigated by Fomin, Greene, Reiner, and Shimozono, the balanced labellings give a natural encoding of reduced ...
Hwanchul Yoo, Taedong Yun
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Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley [PDF]
Algebraic Combinatorics, 2018 We study the action of a differential operator on Schubert polynomials. Using this action, we first give a short new proof of an identity of I. Macdonald (1991). We then prove a determinant conjecture of R. Stanley (2017).
Zachary Hamaker +3 more
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Ehrhart $h^*$-vectors of hypersimplices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We consider the Ehrhart $h^*$-vector for the hypersimplex. It is well-known that the sum of the $h_i^*$ is the normalized volume which equals an Eulerian number. The main result is a proof of a conjecture by R.
Nan Li
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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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The behavior of Stanley depth under polarization [PDF]
, 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 +3 more
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An Edge-Signed Generalization of Chordal Graphs, Free Multiplicities on Braid Arrangements, and Their Characterizations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 In this article, we propose a generalization of the notion of chordal graphs to signed graphs, which is based on the existence of a perfect elimination ordering for a chordal graph. We give a special kind of filtrations of the generalized chordal graphs,
Takuro Abe, Koji Nuida, Yasuhide Numata
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