A Triangulation of the Flow Polytope of the Zigzag Graph

Autor:	Brunner, Rachel, Hanusa, Christopher R. H.
Rok vydání:	2024
Předmět:	Mathematics - Combinatorics Primary: 05A19 05C21 52B12 52B05 52C07 Secondary: 05C05 05C20 05C30 52A38 52B11
Druh dokumentu:	Working Paper
Popis:	We show that the dual graph of the triangulation of the flow polytope of the zigzag graph adorned with the length-reverse-length framing is a subgraph of a grid graph. Through M\'esz\'aros, Morales, and Striker's bijection between simplices of the triangulation, integer flows of a different, supplemental flow polytope, we provide a simple numerical characterization of the adjacency between the triangulation's simplices in terms of their corresponding integer flows. The proofs result from the development of Postnikov and Stanley's sequences of noncrossing bipartite trees as combinatorial objects we call groves. We propose two new statistics derived from this construction that we conjecture recover the $h^*$-polynomial of the flow polytope of the zigzag graph. Comment: 20 pages, 12 figures, 1 table
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2406.20048 Zobrazit plný text záznamu View this record from Arxiv