Séminaire Lotharingien de Combinatoire, B87a (2022), 25 pp.
Cesar Ceballos and Henri Mühle
Revisiting Generalizations of the Dehn-Sommerville Relations
Abstract.
In this survey-like article, we revisit several known versions of the\break 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˜-poly\-nom\-ial:
one that recovers the f˜-polynomial, and one that counts faces according to certain multiplicities.
Received: July 5, 2022.
Revised: July 29, 2022.
Accepted: August 20, 2022.
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