Jean-Christophe Aval - About the determinant of complete non-ambiguous trees

dmtcs:12850 - Discrete Mathematics & Theoretical Computer Science, November 15, 2024, vol. 26:3 - https://doi.org/10.46298/dmtcs.12850
About the determinant of complete non-ambiguous treesArticle

Authors: Jean-Christophe Aval 1

  • 1 Laboratoire Bordelais de Recherche en Informatique

Complete non-ambiguous trees (CNATs) are combinatorial objects which appear in various contexts.Recently, Chen and Ohlig studied the notion of permutations associated to these objects, and proposed a series of nice conjectures.Most of them were proved by Selig and Zhu, through a connection with the abelian sandpile model.But one conjecture remained open, about the distribution of a natural statistic named determinant.We prove this conjecture, in a bijective way.


Volume: vol. 26:3
Section: Combinatorics
Published on: November 15, 2024
Accepted on: October 17, 2024
Submitted on: January 10, 2024
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : HAL
  • Combinatoire enumerative en interaction avec l'algebre, la theorie des nombres et la physique; Funder: French National Research Agency (ANR); Code: ANR-19-CE48-0011

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