Revisiting Generalizations of the Dehn–Sommerville Relations

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

  • Cesar Ceballos - , Graz University of Technology (Author)
  • Henri Mühle - , Institute of Algebra (Author)

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 languageEnglish
Article numberB87a
Number of pages25
JournalSéminaire Lotharingien de Combinatoire : SLC
VolumeB87a
Publication statusPublished - 2023
Peer-reviewedYes

Keywords

Keywords

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

Library keywords