Annals of Combinatorics

, Volume 20, Issue 2, pp 251–281 | Cite as

Symmetries on the Lattice of k-Bounded Partitions

Article

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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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

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

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