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: In addition, we present Dehn-Sommerville relations for 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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