On Garsia-Remmel problem of rook equivalence
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...
متن کاملElliptic Rook and File Numbers
Utilizing elliptic weights, we construct an elliptic analogue of rook numbers for Ferrers boards. Our elliptic rook numbers generalize Garsia and Remmel’s q-rook numbers by two additional independent parameters a and b, and a nome p. The elliptic rook numbers are shown to satisfy an elliptic extension of a factorization theorem which in the classical case was established by Goldman, Joichi and ...
متن کاملThe Inverse Rook Problem on Ferrers Boards
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...
متن کاملThe rook problem on saw-toothed chessboards
A saw-toothed chessboard, or STC for short, is a kind of chessboard whose boundary forms two staircases from left down to right without any hole inside it. A rook at square (i, j) can dominate the squares in row i and in column j . The rook problem of an STC is to determine the minimum number of rooks that can dominate all squares of the STC. In this paper, we model an STC by two particular gra...
متن کاملClassification of Ding’s Schubert Varieties: Finer Rook Equivalence
K. Ding studied a class of Schubert varieties Xλ in type A partial flag manifolds, indexed by integer partitions λ and in bijection with dominant permutations. He observed that the Schubert cell structure of Xλ is indexed by maximal rook placements on the Ferrers board Bλ, and that the integral cohomology groups H∗(Xλ; Z), H ∗(Xμ; Z) are additively isomorphic exactly when the Ferrers boards Bλ,...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00338-j