Abstract:We disprove a long-standing open conjecture due to Simon stating that all skeleta of simplices are extendably shellable. In particular, for every $d \geq 3$ we provide a pure $d$-dimensional shellable simplicial complex which is not shelling completable.
| Subjects: | Combinatorics (math.CO) |
| Cite as: | arXiv:2605.24732 [math.CO] |
| (or arXiv:2605.24732v1 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24732 arXiv-issued DOI via DataCite (pending registration) |
From: Davide Bolognini [view email]
[v1]
Sat, 23 May 2026 20:53:36 UTC (14 KB)
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