Revisiting Generalizations of the Dehn–Sommerville Relations
Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung
Beitragende
Abstract
In this survey-like article, we revisit several known versions of the Dehn–Sommerville relations in the context of: • homology manifolds; • semi-Eulerian complexes; • general simplicial complexes; • balanced semi-Eulerian complexes; and • general completely balanced complexes. In addition, we present Dehn–Sommerville relations for • reciprocal complexes; and • general balanced simplicial complexes; which slightly generalize some of the previous results. Our proofs are uniform, and are based on two simple evaluations of the ˜h-polynomial: one that recovers the ˜f -polynomial, and one that counts faces according to certain multiplicities.
Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | B87a |
| Seitenumfang | 25 |
| Fachzeitschrift | Séminaire Lotharingien de Combinatoire : SLC |
| Jahrgang | B87a |
| Publikationsstatus | Veröffentlicht - 2023 |
| Peer-Review-Status | Ja |
Schlagworte
ASJC Scopus Sachgebiete
Schlagwörter
- balanced complex, Dehn–Sommerville relations, homology manifolds, reciprocal complex, semi-Eulerian complex