Counting the Nontrivial Equivalence Classes of $S_n$ under $\{1234,3412\}$-Pattern-Replacement

Quinn Perian, Bella Xu, Alexander Lu Zhang

We study the $\{1234,3412\}$ pattern-replacement equivalence relation on the set $S_n$ of permutations of length $n$, which is conceptually similar to the Knuth relation. In parti…