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

Abstract

A cascade of dihedral symmetries is hidden in Young's lattice of integer partitions. In fact, for each integer N>2 the Hasse graph of the subposet consisting of the partitions with maximal hook length strictly less than N has the dihedral group of order 2N as its symmetry group. Here a new interpretation of those Hasse graphs is presented, namely as the 1-skeleta of the injective hulls of certain finite metric spaces.

24 pages

References in corpus (2)

• Abelian ideals in a Borel subalgebra of a complex simple Lie algebra
• Cyclic Symmetry of the Scaled Simplex

Cited by in corpus (1)

• Injective hulls of odd cycles