A symmetric chain decomposition of $L(5,n)$

TL;DR

This paper provides a constructive proof demonstrating that Young's lattice $L(5, n)$ can be partitioned into saturated symmetric chains, advancing understanding of its combinatorial structure.

Contribution

It introduces a new constructive method for partitioning $L(5, n)$ into saturated symmetric chains, which was not previously established.

Findings

Young's lattice $L(5, n)$ can be partitioned into saturated symmetric chains

The proof is constructive, providing an explicit partitioning method

Enhances understanding of the combinatorial structure of Young's lattice

Abstract

We give a constructive proof that Young's lattice $L(5, n)$ has a partition into saturated symmetric chains.