Resumen de Sweeping up zeta
We repurpose the main theorem of Thomas and Williams (J Algebr Comb 39(2):225–246, 2014) to prove that modular sweep maps are bijective. We construct the inverse of the modular sweep map by passing through an intermediary set of equitable partitions; motivated by an analogy to stable marriages, we prove that the set of equitable partitions for a fixed word forms a distributive lattice when ordered component wise. We conclude that the general sweep maps defined in Armstrong et al. (Adv Math 284:159–185, 2015) are bijective. As a special case of particular interest, this gives the first proof that the zeta map on rational Dyck paths is a bijection.
