Mirror Variations on Catalan Multijections

Abstract

A Catalan multijection is a way to partition a set of $\binom{2n}{n}$ objects into equivalence classes of size $n+1$, where each equivalence class has exactly one distinct Catalan object. Isaak and Langley investigated when two multijections produced the same partitions in an unpublished manuscript. We propose some new multijections for which we get different partitions from previously discovered multijections.