Revisiting Generalizations of the Dehn–Sommerville Relations
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Contributors
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
| Original language | English |
|---|---|
| Article number | B87a |
| Number of pages | 25 |
| Journal | Séminaire Lotharingien de Combinatoire : SLC |
| Volume | B87a |
| Publication status | Published - 2023 |
| Peer-reviewed | Yes |
Keywords
ASJC Scopus subject areas
Keywords
- balanced complex, Dehn–Sommerville relations, homology manifolds, reciprocal complex, semi-Eulerian complex