Thomas H. Brylawski (1944–2007)

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A Brylawski decomposition for finite ordered sets

Abstmct# A decomposition is given for fini*.e ordered sets P and is shown to bc a unique decomposition in the sense of Brylawski. Hence there exists a universal invariant g(P) for this decomposition , and we c(Dmpute g(P) explicitly. Some modifications of this decomposition are considered ; in particular, one which forms a bidecomposition toecther with disjoint union.

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Introduction Fast similarity search Similarity thresholds Refined structural alignments Concluding remarks Acknowledgements References and recommended reading Abbreviations Copyright

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Consequences of the Brylawski-Lucas Theorem for Binary Matroids

The principal theme of the present paper is to consider isomorphism classes of binary matroids as orbits of a suitable group action . This interpretation is based on a theorem of Brylawski – Lucas . A refinement of the Burnside Lemma is used in order to enumerate these orbits . Ternary matroids are dealt with in much the same way (Section 2) . Counting regular matroids is more dif ficult , but ...

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ژورنال

عنوان ژورنال: European Journal of Combinatorics

سال: 2011

ISSN: 0195-6698

DOI: 10.1016/j.ejc.2011.02.009