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

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