Odd partitions in Young's lattice

Abstract

We show that the subgraph induced in Young's graph by the set of partitions with an odd number of standard Young tableaux is a binary tree. This tree exhibits self-similarities at all scales, and has a simple recursive description.

13 pages, 3 figures, available from http://www.mat.univie.ac.at/~slc/wpapers/s75prasad.html

Cited by in corpus (7)

• Characters of odd degree of symmetric groups
• Representations of symmetric groups with non-trivial determinant
• Restriction of Odd Degree Characters of ${\mathfrak{S}}_n$
• Restriction of odd degree characters and natural correspondences
• Residues modulo powers of two in the Young-Fibonacci lattice
• The Representation Theory of 2-Sylow Subgroups of the Symmetric Group
• Macdonald trees and determinants of representations for finite Coxeter groups