Simplicial complexes of triangular Ferrers boards
نویسندگان
چکیده
منابع مشابه
Rook Poset Equivalence of Ferrers Boards
A natural construction due to K. Ding yields Schubert varieties from Ferrers boards. The poset structure of the Schubert cells in these varieties is equal to the poset of maximal rook placements on the Ferrers board under the Bruhat order. We determine when two Ferrers boards have isomorphic rook posets. Equivalently, we give an exact categorization of when two Ding Schubert varieties have iden...
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Let C(n; N) = R H N tr Z 2n (dZ) denote a matrix integral by a U(N)-invariant gaussian measure on the space H N of hermitian N N matrices. The integral is known to be always a positive integer. We derive a simple combinatorial interpretation of this integral in terms of rook conngurations on Ferrers boards. The formula C(n; N) = (2n ? 1)!! n X k=0 N k + 1 n k 2 k found by J. Harer and D. Zagier...
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Rook polynomials have been studied extensively since 1946, principally as a method for enumerating restricted permutations. However, they have also been shown to have many fruitful connections with other areas of mathematics, including graph theory, hypergeometric series, and algebraic geometry. It is known that the rook polynomial of any board can be computed recursively. [19, 18] The naturall...
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In this paper we provide an explicit formula for calculating the boolean number of a Ferrers graph. By previous work of the last two authors, this determines the homotopy type of the boolean complex of the graph. Specializing to staircase shapes, we show that the boolean numbers of the associated Ferrers graphs are the Genocchi numbers of the second kind, and obtain a relation between the Legen...
متن کاملBruhat intervals as rooks on skew Ferrers boards
We characterise the permutations π such that the elements in the closed lower Bruhat interval [id, π] of the symmetric group correspond to nontaking rook configurations on a skew Ferrers board. It turns out that these are exactly the permutations π such that [id, π] corresponds to a flag manifold defined by inclusions, studied by Gasharov and Reiner. Our characterisation connects the Poincaré p...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2012
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-012-0385-x