English

Non-extendably shellable skeleta of simplices

Combinatorics 2026-05-26 v1

Abstract

We disprove a long-standing open conjecture due to Simon stating that all skeleta of simplices are extendably shellable. In particular, for every d3d \geq 3 we provide a pure dd-dimensional shellable simplicial complex which is not shelling completable.

Cite

@article{arxiv.2605.24732,
  title  = {Non-extendably shellable skeleta of simplices},
  author = {Davide Bolognini and Paolo Sentinelli},
  journal= {arXiv preprint arXiv:2605.24732},
  year   = {2026}
}
R2 v1 2026-07-22T07:30:21.756Z