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Odd partitions in Young’s lattice. (English) Zbl 1339.05014
Summary: We show that the subgraph induced in a 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.

MSC:
05A15 Exact enumeration problems, generating functions
05A17 Combinatorial aspects of partitions of integers
05E10 Combinatorial aspects of representation theory
20C30 Representations of finite symmetric groups
20B30 Symmetric groups
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