Symmetries on the lattice of $k$-bounded partitions
Combinatorics
2014-10-09 v3
Abstract
In 2002 R. Suter identified a dihedral symmetry on certain order ideals in Young's lattice and gave a combinatorial action on the partitions in these order ideals. Viewing this result geometrically, the order ideals can be seen to be seen to be in bijection with the alcoves in a 2-fold dilation in the geometric realization of the affine symmetric group. By considering the m-fold dilation we observe a larger set of order ideals in the k-bounded partition lattice that was considered by L. Lapointe, A. Lascoux, and J. Morse in the study of k-Schur functions. We identify the order ideal and the cyclic action on it explicitly in a geometric and combinatorial form.
Keywords
Cite
@article{arxiv.1111.2783,
title = {Symmetries on the lattice of $k$-bounded partitions},
author = {Chris Berg and Nathan Williams and Mike Zabrocki},
journal= {arXiv preprint arXiv:1111.2783},
year = {2014}
}