The steep-bounce zeta map in parabolic Cataland

Wenjie Fang, Cesar Ceballos, Henri Mühle

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


As a classical object, the Tamari lattice has many generalizations, including ν-Tamari lattices and parabolic Tamari lattices. In this article, we unify these general-izations in a bijective fashion. We first prove that parabolic Tamari lattices are isomorphic to ν-Tamari lattices for bounce paths ν. We then introduce a new combinatorialobject called “left-aligned colored tree”, and show that it provides a bijective bridge between various parabolic Catalan objects and certain nested pairs of Dyck paths. As a consequence, we prove the Steep-Bounce Conjecture using a generalization of the famous zeta map in q,t-Catalan combinatorics.
Original languageEnglish
Title of host publicationProceedings of the 31st Conference on Formal Power Series and Algebraic Combinatorics
Subtitle of host publicationSéminaire Lotharingien de Combinatoire
Number of pages12
Publication statusPublished - 2019
EventFPSAC 2019 - Ljubljana, Slovenia
Duration: 1 Jul 20195 Jul 2019


ConferenceFPSAC 2019


  • parabolic Tamari lattice
  • ν-Tamari lattice
  • bijection
  • left-aligned colorable tree
  • zeta map


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