Results 21 to 30 of about 294 (153)
Higher Bruhat Orders in Type B [PDF]
The Electronic Journal of Combinatorics, 2016 Motivated by the geometry of hyperplane arrangements, Manin and Schechtman defined for each integer $n \geq 1$ a hierarchy of finite partially ordered sets $B(n, k),$ indexed by positive integers $k$, called the higher Bruhat orders. The poset $B(n, 1)$ is naturally identified with the weak left Bruhat order on the symmetric group $S_n$, each $B(n, k)$
Shelley-Abrahamson, Seth +1 more
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The Coincidence of the Bruhat Order and the Secondary Bruhat Order on $$\mathcal {A}(n,k)$$
Order, 2023 Given a positive integer $n$ and a nonnegative integer $k$ with $k\leq n$, we denote by $\mathcal{A}(n,k)$ the class of all $n$-by-$n$ $(0,1)$-matrices with constant row and column sums $k$. In this paper, we show that the Bruhat order and the secondary Bruhat order coincide on $\mathcal{A}(n,k)$ if and only if either $0\leq n\leq 5$ or $k\in\{0,1,2,n ...
Zhang, Tao, Yu, Houyi
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The Bruhat order on conjugation-invariant sets of involutions in the symmetric group [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 12 pages, 3 ...
Mikael Hansson
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Quasisymmetric Schur functions and modules of the $0$-Hecke algebra [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We define a $0$-Hecke action on composition tableaux, and then use it to derive $0$-Hecke modules whose quasisymmetric characteristic is a quasisymmetric Schur function.
Vasu Tewari, Stephanie van Willigenburg
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Alignments, crossings, cycles, inversions, and weak Bruhat order in permutation tableaux of type $B$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Alignments, crossings and inversions of signed permutations are realized in the corresponding permutation tableaux of type $B$, and the cycles of signed permutations are understood in the corresponding bare tableaux of type $B$.
Soojin Cho, Kyoungsuk Park
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A $t$-generalization for Schubert Representatives of the Affine Grassmannian [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We introduce two families of symmetric functions with an extra parameter $t$ that specialize to Schubert representatives for cohomology and homology of the affine Grassmannian when $t=1$.
Avinash J. Dalal, Jennifer Morse
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The Bruhat rank of a binary symmetric staircase pattern
Open Mathematics, 2016 In this work we show that the Bruhat rank of a symmetric (0,1)-matrix of order n with a staircase pattern, total support, and containing In, is at most 2. Several other related questions are also discussed. Some illustrative examples are presented.
Du Zhibin, da Fonseca Carlos M.
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The ABC's of affine Grassmannians and Hall-Littlewood polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We give a new description of the Pieri rule for $k$-Schur functions using the Bruhat order on the affine type-$A$ Weyl group. In doing so, we prove a new combinatorial formula for representatives of the Schubert classes for the cohomology of affine ...
Avinash J. Dalal, Jennifer Morse
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Linear Algebra and its Applications, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Brualdi, Richard A., Fritscher, Eliseu
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An improved tableau criterion for Bruhat order [PDF]
The Electronic Journal of Combinatorics, 1996 To decide whether two permutations are comparable in Bruhat order of $S_n$ with the well-known tableau criterion requires $\binom{n}{2}$ comparisons of entries in certain sorted arrays. We show that to decide whether $x\le y$ only $d_1+d_2+...+d_k$ of these comparisons are needed, where $\{d_1,d_2,...,d_k\} = \{i|x(i)>x(i+1)\}$.
Francesco Brenti, Anders Björner
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