48 citations · 129 across the 9 of their papers we have counts for
3 papers · 1 filter
Cluster Algebras of Type , Tropical Planes, and the Positive Tropical Grassmannian
Sarah B. Brodsky, Cesar Ceballos, Jean-Philippe Labbé
We show that the number of combinatorial types of clusters of type modulo reflection-rotation is exactly equal to the number of combinatorial types of tropical planes in $\ma…
Hirsch polytopes with exponentially long combinatorial segments
Jean-Philippe Labbé, Thibault Manneville, Francisco Santos
In their paper proving the Hirsch bound for flag normal simplicial complexes (Math. Oper.~Res.~2014) Adiprasito and Benedetti define the notion of~\emph{combinatorial segment}. The…
On inversion sets and the weak order in Coxeter groups
Christophe Hohlweg, Jean-Philippe Labbé
In this article, we investigate the existence of joins in the weak order of an infinite Coxeter group W. We give a geometric characterization of the existence of a join for a subse…