The steep-bounce zeta map in parabolic Cataland

Wenjie Fang, Cesar Ceballos, Henri Mühle

Publikation: KonferenzbeitragAbstractForschungBegutachtung

Abstract

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.
Originalspracheenglisch
PublikationsstatusAngenommen/In Druck - 2019

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Bounce
Bijective
Dyck Paths
Combinatorics
Isomorphic
Path

Schlagwörter

    Dies zitieren

    Fang, W., Ceballos, C., & Mühle, H. (Angenommen/Im Druck). The steep-bounce zeta map in parabolic Cataland.

    The steep-bounce zeta map in parabolic Cataland. / Fang, Wenjie; Ceballos, Cesar; Mühle, Henri.

    2019.

    Publikation: KonferenzbeitragAbstractForschungBegutachtung

    Fang, W, Ceballos, C & Mühle, H 2019, 'The steep-bounce zeta map in parabolic Cataland'.
    Fang W, Ceballos C, Mühle H. The steep-bounce zeta map in parabolic Cataland. 2019.
    Fang, Wenjie ; Ceballos, Cesar ; Mühle, Henri. / The steep-bounce zeta map in parabolic Cataland.
    @conference{c740b209c170410d8cf273bc13f13e48,
    title = "The steep-bounce zeta map in parabolic Cataland",
    abstract = "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.",
    keywords = "parabolic Tamari lattice, ν-Tamari lattice, bijection, left-aligned colorable tree, zeta map",
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    T1 - The steep-bounce zeta map in parabolic Cataland

    AU - Fang, Wenjie

    AU - Ceballos, Cesar

    AU - Mühle, Henri

    PY - 2019

    Y1 - 2019

    N2 - 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.

    AB - 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.

    KW - parabolic Tamari lattice

    KW - ν-Tamari lattice

    KW - bijection

    KW - left-aligned colorable tree

    KW - zeta map

    M3 - Abstract

    ER -