Symmetries on the Lattice of k-Bounded Partitions

Chris Berg; Nathan Williams; Mike Zabrocki

doi:10.1007/s00026-016-0307-z

Annals of Combinatorics

June 2016, Volume 20, Issue 2, pp 251–281

Symmetries on the Lattice of k-Bounded Partitions

Authors
Authors and affiliations

Chris Berg
Nathan Williams
Mike ZabrockiEmail author

Article

First Online:: 13 February 2016

Received:: 16 June 2012

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Abstract

In 2002, Suter [25] 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 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 Lapointe, Lascoux, and Morse [14] 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

affine reflection groups symmetry

Mathematics Subject Classification

05E18 51F15

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Authors and Affiliations

Chris Berg
- 1
Nathan Williams
- 2
Mike Zabrocki
- 3
- 4
Email author

1.The Laboratoire de combinatoire et d’informatique mathétique (LaCIM)GoogleMontrealCanada
2.Department of MathematicsUniversité du Québec à MontréalMontréalCanada
3.Fields InstituteTorontoCanada
4.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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Cite this article as:: Berg, C., Williams, N. & Zabrocki, M. Ann. Comb. (2016) 20: 251. doi:10.1007/s00026-016-0307-z

Symmetries on the Lattice of k-Bounded Partitions

Abstract

Keywords

Mathematics Subject Classification

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