Report Number: CS-TR-79-763
Institution: Stanford University, Department of Computer Science
Title: A symmetric chain decomposition of L(4,n)
Author: West, Douglas B.
Date: August 1979
Abstract: L(m,n) is the set of integer m-tuples ($a_1$,...,$a_m$) with $0\leq a_1 \leq ...\leq a_m \leq n$, ordered by $\underline{a} \leq \underline{b}$ when $a_i\leq b_i$ for all i. R. Stanley conjectured that L(m,n) is a symmetric chain order for all (m,n). We verify this by construction for m = 4.
http://i.stanford.edu/pub/cstr/reports/cs/tr/79/763/CS-TR-79-763.pdf