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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Binary supersolvable matroids and modular constructions


Author: Günter M. Ziegler
Journal: Proc. Amer. Math. Soc. 113 (1991), 817-829
MSC: Primary 05B35; Secondary 05C38, 06C10
DOI: https://doi.org/10.1090/S0002-9939-1991-1068134-3
MathSciNet review: 1068134
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Abstract: Let $ \mathcal{M}$ be the class of binary matroids without a Fano plane as a submatroid. We show that every supersolvable matroid in $ \mathcal{M}$ is graphic, corresponding to a chordal graph. Then we characterize the case that the modular join of two matroids is supersolvable. This is used to study modular flats and modular joins of binary supersolvable matroids. We decompose supersolvable matroids in $ \mathcal{M}$ as modular joins with respect to hyperplanes. For such matroids every modular flat is contained in a maximal chain of modular flats, and thus modular joins are again supersolvable.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1068134-3
Article copyright: © Copyright 1991 American Mathematical Society