Revisiting Generalizations of the Dehn–Sommerville Relations

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

  • Cesar Ceballos - , Technische Universität Graz (Autor:in)
  • Henri Mühle - , Institut für Algebra (Autor:in)

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

OriginalspracheEnglisch
AufsatznummerB87a
Seitenumfang25
FachzeitschriftSéminaire Lotharingien de Combinatoire : SLC
JahrgangB87a
PublikationsstatusVeröffentlicht - 2023
Peer-Review-StatusJa

Schlagworte

Schlagwörter

  • balanced complex, Dehn–Sommerville relations, homology manifolds, reciprocal complex, semi-Eulerian complex

Bibliotheksschlagworte