Abstract:Framing triangulations of unit flow polytopes have received a great deal of recent study with rich connections to various generalizations of Catalan and Cambrian combinatorics as well as volume and h*-polynomial formulas. This story has largely been restricted to unit flow polytopes, with only two recent works giving descriptions of framing triangulations on classes of non-unit flow polytopes. In this article we introduce the first theory of (unimodular) framing triangulations for arbitrary integer flow polytopes. We will observe some pathologies in general examples which are impossible in the unit case, and propose in response a class of "well-ordered" framing triangulations which we expect to inherit key properties from the unit case while still containing all settings of framing triangulations existing in the literature.
| Comments: | 31 pages, 11 figures, comments welcome |
| Subjects: | Combinatorics (math.CO) |
| MSC classes: | 05C21 (primary) 05E45, 52B11 (secondary) |
| Cite as: | arXiv:2605.24328 [math.CO] |
| (or arXiv:2605.24328v1 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24328 arXiv-issued DOI via DataCite (pending registration) |
From: Jonah Berggren [view email]
[v1]
Sat, 23 May 2026 01:16:56 UTC (1,208 KB)
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