21 research outputs found
Cyclic derangements
A classic problem in enumerative combinatorics is to count the number of
derangements, that is, permutations with no fixed point. Inspired by a recent
generalization to facet derangements of the hypercube by Gordon and McMahon, we
generalize this problem to enumerating derangements in the wreath product of
any finite cyclic group with the symmetric group. We also give q- and (q,
t)-analogs for cyclic derangements, generalizing results of Brenti and Gessel.Comment: 14 page
A Littlewood-Richardson rule for Grassmannian Schubert varieties
We propose a combinatorial model for the Schubert structure constants of the
complete flag manifold when one of the factors is Grassmannian.Comment: 6 pages, 2 figures - Final versio
A bijective proof of Kohnert's rule for Schubert polynomials
Kohnert proposed the first monomial positive formula for Schubert polynomials
as the generating polynomial for certain unit cell diagrams obtained from the
Rothe diagram of a permutation. Billey, Jockusch and Stanley gave the first
proven formula for Schubert polynomials as the generating polynomial for
compatible sequences of reduced words of a permutation. In this paper, we give
an explicit bijection between these two models, thereby definitively proving
Kohnert's rule for Schubert polynomials.Comment: 8 pages, 7 figures (examples added, minor corrections
Recommended from our members
A bijective proof of Kohnert's rule for Schubert polynomials
Kohnert proposed a formula for Schubert polynomials as the generating polynomial for certain unit cell diagrams obtained from the diagram of a permutation. Billey, Jockusch and Stanley proved a formula for Schubert polynomials as the generating polynomial for compatible sequences of reduced words. In this paper, we give an explicit bijection between these two models, thereby proving Kohnert's rule for Schubert polynomials.Mathematics Subject Classifications: 05A05, 05A19, 14N10, 14N1