# Equipopularity in the Separable Permutations

with
Michael Albert and
Jay Pantone

## Abstract:

When two patterns occur equally often in a set of permutations, we say that
these patterns are equipopular. Using both structural and analytic tools, we
classify the equipopular patterns in the set of separable permutations. In
particular, we show that the number of equipopularity classes for length $n$ patterns
in the separable permutations is equal to the number of partitions of $n-1$.