The Electronic Journal of Combinatorics· 2026Q1
A Triangulation of the Flow Polytope of the Zigzag Graph
- 1citations
- Q1SCImago
- 2026year
Short summary
The dual graph of a specific triangulation of the zigzag graph's flow polytope is a subgraph of a grid graph.
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Key points
- The dual graph of the flow polytope's triangulation is a subgraph of a grid graph.
- A bijection connects triangulation simplices to integer flows, simplifying adjacency characterization.
- The construction utilizes sequences of noncrossing bipartite trees (groves).
- Two new statistics are proposed, conjectured to recover the $h^*$-polynomial.
AI-generated from the title and abstract; the full text is not read.
Abstract
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 Mészáros, 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.
The authors' abstract, as published at the source. The Electronic Journal of Combinatorics, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics