Young Walls of Type $D^(2)_n+1$ and Strict Partitions

TL;DR

This paper establishes a surprising connection between the enumeration of reduced Young walls of a certain type and strict partitions, leading to new generalizations of Euler's partition identity.

Contribution

It demonstrates that the count of reduced Young walls of type D^{(2)}_{n+1} is independent of n and matches the number of strict partitions, linking representation theory with partition identities.

Findings

Number of reduced Young walls is independent of n.

Count matches the number of strict partitions.

Provides a new family of Euler's partition identity generalizations.

Abstract

We show that the number of reduced Young walls of type $D_{n+1}^{(2)}$ with $m$ blocks is independent of $n$ and the same as the number of strict partitions of $m$. Thus the principally specialized character $\chi_n^{\Lambda_0}(t)$ of $V(\Lambda_0)$ over $U_q(D_{n+1}^{(2)})$ can be interpreted as a generating function for strict partitions. Hence we obtain an infinite family of generalizations of Euler's partition identity.