English

A note on M\"{o}bius functions of upho posets

Combinatorics 2022-06-06 v3

Abstract

A poset is called upper homogeneous (or "upho") if every principal order filter of the poset is isomorphic to the whole poset. We observe that the rank and characteristic generating functions of upho posets are multiplicative inverses of one another.

Keywords

Cite

@article{arxiv.2202.12103,
  title  = {A note on M\"{o}bius functions of upho posets},
  author = {Sam Hopkins},
  journal= {arXiv preprint arXiv:2202.12103},
  year   = {2022}
}

Comments

5 pages; v3: improved exposition thanks to referee comments, to be published in Elec. J. Comb

R2 v1 2026-06-24T09:52:31.009Z