Cyclic Symmetry of the Scaled Simplex

Abstract

Let Z_m^k consist of the m^k alcoves contained in the m-fold dilation of the fundamental alcove of the type A_k affine hyperplane arrangement. As the fundamental alcove has a cyclic symmetry of order (k+1), so does Z_m^k. By bijectively exchanging the natural poset structure of Z_m^k for a natural cyclic action on a set of words, we prove an instance of the cyclic sieving phenomenon.

19 pages, 14 figures

References in corpus (1)

• Abelian ideals in a Borel subalgebra of a complex simple Lie algebra

Cited by in corpus (1)

• Young's lattice and dihedral symmetries revisited: Möbius strips and metric geometry