Revisiting Generalizations of the Dehn-Sommerville Relations

Cesar Ceballos, Henri Mühle

Research output: Contribution to journalArticlepeer-review


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-poly-
nomial: one that recovers the ̃f -polynomial, and one that counts faces according to certain multiplicities.
Original languageEnglish
Article numberB87a
Number of pages25
JournalSéminaire Lotharingien de Combinatoire
Publication statusPublished - 2022


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