Decorated hypertrees

TL;DR

This paper explores decorated hypertrees, linking them to weighted hypertrees used in algebraic topology and group theory, and provides enumeration methods via box trees, advancing understanding of their combinatorial and algebraic properties.

Contribution

It introduces a comprehensive study of decorated hypertrees, establishing their enumeration through box trees and connecting them to weighted hypertrees in algebraic contexts.

Findings

Linked decorated hypertrees to weighted hypertrees in homology studies.

Developed enumeration techniques for decorated hypertrees using box trees.

Provided insights into the algebraic and combinatorial structures of hypertrees.

Abstract

C. Jensen, J. McCammond and J. Meier have used weighted hypertrees to compute the Euler characteristic of a subgroup of the automorphism group of a free product. Weighted hypertrees also appear in the study of the homology of the hypertree poset. We link them to decorated hypertrees after a general study on decorated hypertrees, which we enumerate using box trees.---C. Jensen, J. McCammond et J. Meier ont utilis\'e des hyperarbres pond\'er\'es pour calculer la caract\'eristique d'Euler d'un sous-groupe du groupe des automorphismes d'un produit libre. Un autre type d'hyperarbres pond\'er\'es appara\^it aussi dans l'\'etude de l'homologie du poset des hyperarbres. Nous \'etudions les hyperarbres d\'ecor\'es puis les comptons \`a l'aide de la notion d'arbre en bo\^ite avant de les relier aux hyperarbres pond\'er\'es.