More Shattering News
Combinatorics
2026-03-20 v1
Abstract
An ordered variant of the well-known set theory concept of shattering was introduced by Anstee, R\'onyai, and Sali. In this paper, we prove several new results related to order shattering. Given a family of subsets of , we show that , the family of all sets order shattered by , coincides with , the family obtained from by the down-shift operation. We then give a full characterization of all sets that can be order shattered by some -Sperner family. Finally, we completely determine .
Keywords
Cite
@article{arxiv.2603.18708,
title = {More Shattering News},
author = {Attila Sali and Jun Yan},
journal= {arXiv preprint arXiv:2603.18708},
year = {2026}
}