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arXiv · 2605.24732

Non-extendably shellable skeleta of simplices

Davide Bolognini·Paolo Sentinelli
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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.

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Davide Bolognini, Paolo Sentinelli. 2026-07-31. Non-extendably shellable skeleta of simplices. https://arxiv.org/abs/2605.24732

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