On geometric semilattices

Michelle L. Wachs, James W. Walker

Research output: Contribution to journalArticle

36 Scopus citations

Abstract

We define geometric semilattices, a generalization of geometric lattices. The poset of independent sets of a matroid is another example. We prove several axiomatic and constructive characterizations, for example: geometric semilattices are those semilattices obtained by removing a principal filter from a geometric lattice. We also show that all geometric semilattices are shellable, unifying and extending several previous results.

Original languageEnglish (US)
Pages (from-to)367-385
Number of pages19
JournalOrder
Volume2
Issue number4
DOIs
StatePublished - Dec 1 1985

    Fingerprint

Keywords

  • AMS (MOS) subject classifications (1980): 06A10, 06B99, 06C10
  • Geometric lattice
  • Möbius function
  • matroid
  • shellable
  • strong map

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Theory and Mathematics

Cite this