Browsing by Author "Grinberg, Darij"

Now showing 1 - 5 of 5
  • Thumbnail Image
    Item
    Birational Rowmotion on a Rectangle over a Noncommutative Ring
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2022) Grinberg, Darij; Roby, Tom
    We extend the periodicity of birational rowmotion for rectangular posets to the case when the base field is replaced by a noncommutative ring (under appropriate conditions). This resolves a conjecture from 2014. The proof uses a novel approach and is fully self-contained.
  • Thumbnail Image
    Item
    Hopf Algebras in Combinatorics, Volume 1
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2020) Grinberg, Darij; Reiner, Victor
    [no abstract available]
  • Thumbnail Image
    Item
    Hopf Algebras in Combinatorics, Volume 2
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2020) Grinberg, Darij; Reiner, Victor
    [no abstract available]
  • Thumbnail Image
    Item
    The Elser Nuclei Sum Revisited
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2021) Grinberg, Darij
    Fix a finite undirected graph Γ and a vertex v of Γ. Let E be the set of edges of Γ. We call a subset F of E pandemic if each edge of Γ has at least one endpoint that can be connected to v by an F-path (i.e., a path using edges from F only). In 1984, Elser showed that the sum of (−1)|F| over all pandemic subsets F of E is 0 if E≠∅. We give a simple proof of this result via a sign-reversing involution, and discuss variants, generalizations and a refinement using discrete Morse theory.
  • Thumbnail Image
    Item
    The Pelletier-Ressayre Hidden Symmetry for Littlewood-Richardson Coefficients
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2020) Grinberg, Darij
    We prove an identity for Littlewood–Richardson coefficients conjectured by Pelletier and Ressayre. The proof relies on a novel birational involution defined over any semifield.