Rook placements and generalized partition varieties

DOI10.1016/S0012-365X(96)00287-7zbMath0887.05057OpenAlexW2063281630MaRDI QIDQ1377680

Kequan Ding

Publication date: 28 April 1998

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0012-365x(96)00287-7

zbMATH Keywords

flag manifoldBruhat orderprojective varietyGrassmannian manifoldSchubert cellspartition varietyrook length polynomial

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Permutations, words, matrices (05A05) Algebraic combinatorics (05E99) Grassmannians, Schubert varieties, flag manifolds (14M15)

Related Items

Springer fibers and Schubert points ⋮ Hessenberg varieties of parabolic type ⋮ Elliptic extensions of the alpha-parameter model and the rook model for matchings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bijective methods in the theory of finite vector spaces
• A maj statistic for set partitions
• \(p,q\)-Stirling numbers and set partition statistics
• Unimodality of Gaussian coefficients: A constructive proof
• The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field
• Q-counting rook configurations and a formula of Frobenius
• A \(q\)-analog of the exponential formula
• Rook theory. III: Rook polynomials and the chromatic structure of graphs
• Rook theory. V: Rook polynomials, Möbius inversion and the umbral calculus
• Rook placements and cellular decomposition of partition varieties
• Invisible permutations and rook placements on a Ferrers board
• On Garsia-Remmel problem of rook equivalence
• The q-Stirling numbers of first and second kinds
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
• Characteristic Classes. (AM-76)
• Rook Theory. I.: Rook Equivalence of Ferrers Boards
• A Theorem on Reciprocal Polynomials with Applications to Permutations and Compositions
• Rook Theory. II: Boards of Binomial Type
• Rook Theory-IV. Orthogonal Sequences of Rook Polynomials