On geometric semilattices

Michelle L Galloway, James W. Walker

Research output: Contribution to journalArticle

36 Citations (Scopus)

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 1985

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Semilattice
Geometric Lattice
Independent Set
Matroid
Poset
Filter

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On geometric semilattices. / Galloway, Michelle L; Walker, James W.

In: Order, Vol. 2, No. 4, 12.1985, p. 367-385.

Research output: Contribution to journalArticle

Galloway, ML & Walker, JW 1985, 'On geometric semilattices', Order, vol. 2, no. 4, pp. 367-385. https://doi.org/10.1007/BF00367425
Galloway, Michelle L ; Walker, James W. / On geometric semilattices. In: Order. 1985 ; Vol. 2, No. 4. pp. 367-385.
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