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Geometric lattice

Known as: Matroid lattice 
In the mathematics of matroids and lattices, a geometric lattice is a finite atomistic semimodular lattice, and a matroid lattice is an atomistic… Expand
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Highly Cited
2012
Highly Cited
2012
Abstract Let G be a finite group of order m ≥ 1 . A Dowling lattice Q n ( G ) is the geometric lattice of rank n over G . In this… Expand
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2012
2012
Covering-based rough set theory is a useful tool to deal with inexact, uncertain, or vague knowledge in information systems… Expand
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2010
2010
Abstract Extending former results by G. Gratzer and E.W. Kiss (1986) [5] and M. Wild (1993) [9] on finite (upper) semimodular… Expand
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2004
2004
Abstract The flag Whitney numbers (also referred to as the flag f-numbers) of a geometric lattice count the number of chains… Expand
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1986
1986
A geometric lattice G is said to be modularly complemented if for every point in G , there exists a modular copoint not… Expand
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Highly Cited
1985
Highly Cited
1985
1. IN~~DUCTION During the last 20 years, there has been a great deal of research concerning designs with A= 1 admitting 2… Expand
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1975
1975
Publisher Summary This chapter discusses Whitney numbers of geometric lattices. There is a homology theory on the category of… Expand
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1974
1974
Abstract Let G be an n-dimensional geometric lattice. Suppose that 1 ⩽ e, f ⩽ n − 1, e + f ⩾ n, but e and f are not both n − 1… Expand
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Highly Cited
1972
Highly Cited
1972
A construction based on work by Tutte and Grothendieck is applied to a decomposition on combinatorial pregeometries in order to… Expand
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Highly Cited
1971
Highly Cited
1971
Let L be a finite geometric lattice of rank n with rank function r. (For definitions, see e.g., [3, Chapter 2], [4], or [1… Expand
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