The greedy flip tree of a subword complex

TL;DR

This paper introduces a canonical spanning tree for the ridge graph of a subword complex in Coxeter groups, enabling efficient enumeration of facets through a greedy flip-based algorithm extension.

Contribution

It presents a new spanning tree structure for subword complexes and extends the greedy flip algorithm to facilitate facet enumeration.

Findings

Defines properties of greedy facets in subword complexes

Establishes a canonical spanning tree of the ridge graph

Provides an enumeration scheme for facets

Abstract

We describe a canonical spanning tree of the ridge graph of a subword complex on a finite Coxeter group. It is based on properties of greedy facets in subword complexes, defined and studied in this paper. Searching this tree yields an enumeration scheme for the facets of the subword complex. This algorithm extends the greedy flip algorithm for pointed pseudotriangulations of points or convex bodies in the plane.