Sweeping up zeta

• Hugh Thomas ^[2] ; Nathan Williams ^[1]
  1. [1] University of Texas at Dallas

     University of Texas at Dallas

     Estados Unidos

     
  2. [2] Université du Québec à Montéal
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 3, 2018, págs. 2003-2034
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • 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.