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Peer-reviewedCC BY 4.0The Electronic Journal of Combinatorics

A Triangulation of the Flow Polytope of the Zigzag Graph

  • Rachel Brunner
  • Christopher R. H. Hanusa
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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.

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Cite

BibTeXRIS
BibTeX
@article{brunner2026triangulation,
  title = {{A Triangulation of the Flow Polytope of the Zigzag Graph}},
  author = {Rachel Brunner and Christopher R. H. Hanusa},
  journal = {The Electronic Journal of Combinatorics},
  year = {2026},
  month = oct,
  doi = {10.37236/13162},
  url = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p10},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Triangulation of the Flow Polytope of the Zigzag Graph
AU  - Rachel Brunner
AU  - Christopher R. H. Hanusa
PY  - 2026
DA  - 2026/10/09
JO  - The Electronic Journal of Combinatorics
DO  - 10.37236/13162
UR  - https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p10
AB  - 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.
SN  - 1077-8926
ER  -