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Abstract: A geometric lattice is a frame if its matroid, possibly after enlargement, has a basis such that every atom lies under a join of at most two basis elements. Examples include all subsets of a classical root system. Using the fact that finitary frame matroids are the bias matroids of biased graphs, we characterize modular coatoms in frames of finite rank and we describe explicitly the frames that are supersolvable. We apply the characterizations to three kinds of example: one generalizes the root ... (Update)
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BibTeX entry: (Update)
T. Zaslavsky, Supersolvable frame-matroid and graphic-lift lattices. Submitted. http://citeseer.ist.psu.edu/zaslavsky96supersolvable.html More
@misc{ zaslavsky-supersolvable,
author = "T. Zaslavsky",
title = "Supersolvable frame-matroid and graphic-lift lattices",
text = "T. Zaslavsky, Supersolvable frame-matroid and graphic-lift lattices. Submitted.",
url = "citeseer.ist.psu.edu/zaslavsky96supersolvable.html" }
Citations (may not include all citations):488 Algorithmic Graph Theory and Perfect Graphs (context) - Golumbic - 1980
158 Matroid theory (context) - Welsh - 1976
157 Advanced Combinatorics (context) - Comtet - 1974
126 Oxford University Press (context) - Oxley, Theory - 1992
90 On rigid circuit graphs (context) - Dirac - 1961
25 Supersolvable lattices (context) - Stanley - 1972
18 Modular constructions for combinatorial geometries (context) - Brylawski - 1975
16 Broken circuit complexes: factorizations and generalizations (context) - Bjorner, Ziegler - 1991
14 The geometry of root systems and signed graphs (context) - Zaslavsky - 1981
14 Generalized exponents of a free arrangement of hyperplanes a.. (context) - Terao - 1981
12 A class of geometric lattices based on finite groups (context) - Dowling - 1973
8 personal communication (context) - Bonin
7 Modular elements of geometric lattices (context) - Stanley - 1971
7 Combinatorics of inductively factored arrangements (context) - Jambu, Paris - 1995
7 Factorizations of Orlik-Solomon algebras (context) - Terao - 1992
6 Arrangements of hyperplanes and their freeness (context) - Terao - 1980
6 A generalization of semimodular supersolvable lattices - Bennett, Sagan
4 Algebraic combinatorics of hyperplane arrangements (context) - Ziegler - 1987
3 Tractable partially ordered sets derived from root systems a.. - Hanlon, Zaslavsky
2 The greedy algorithm for finitary and cofinitary matroids (context) - Klee - 1971
2 A combinatorial construction of posets that intertwine the i.. (context) - Hanlon - 1988
2 An affine representation for transversal geometries (context) - Brylawski - 1975
2 On subgraphs as matroid cells (context) - oes-Pereira - 1972
2 Inductively factored signed-graphic arrangements of hyperpla.. - Bailey
2 probl`eme des m'enages (context) - Kaplansky, the - 1943
1 Frame matroids and biased graphs (context) - Zaslavsky - 1994
1 Geometric lattices of structured partitions: III (context) - Zaslavsky - 1985
1 Dowling group geometries and the critical problem (context) - Whittle - 1989
Documents on the same site (http://math.binghamton.edu/zaslav/publ.html): More
Biased Graphs: IV. Geometrical Realizations - Zaslavsky (1986) (Correct)
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