A Classification of Modularly Complemented Geometric Lattices

Jeff Kahn; Joseph P.S. Kung

doi:10.1016/S0195-6698(86)80029-4

A Classification of Modularly Complemented Geometric Lattices

Jeff Kahn, Joseph P.S. Kung

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

A geometric lattice G is said to be modularly complemented if for every point in G, there exists a modular copoint not containing it. We prove that a connected modularly complemented geometric lattice of rank at least four is either a Dowling lattice or the lattice of flats of a projective geometry with some of its points deleted.

Original language	English (US)
Pages (from-to)	243-248
Number of pages	6
Journal	European Journal of Combinatorics
Volume	7
Issue number	3
DOIs	https://doi.org/10.1016/S0195-6698(86)80029-4
State	Published - 1986

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1016/S0195-6698(86)80029-4

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title = "A Classification of Modularly Complemented Geometric Lattices",

abstract = "A geometric lattice G is said to be modularly complemented if for every point in G, there exists a modular copoint not containing it. We prove that a connected modularly complemented geometric lattice of rank at least four is either a Dowling lattice or the lattice of flats of a projective geometry with some of its points deleted.",

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AB - A geometric lattice G is said to be modularly complemented if for every point in G, there exists a modular copoint not containing it. We prove that a connected modularly complemented geometric lattice of rank at least four is either a Dowling lattice or the lattice of flats of a projective geometry with some of its points deleted.

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JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

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A Classification of Modularly Complemented Geometric Lattices

Abstract

All Science Journal Classification (ASJC) codes

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