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On the activities of p-basis of matroid perspectives

Kayibi, Koko K.; Pirzada, S.

Authors

Koko K. Kayibi

S. Pirzada



Abstract

There is a renewed interest in matroid perspectives, either for their relevance in other fields of combinatorics and topology, or their applications in engineering. But, like for most of the Tutte invariants, computing the Tutte polynomial of matroid perspectives is #P-hard. Hence the importance of results whose applications would help to speed up computations. In the present paper, we show that a pseudobasis of a matroid perspective can be decomposed by a cyclic flat into two subsets, one of which has zero internal activity and the other has zero external activity. Apart from its own interest in understanding the internal structures of matroid perspective, this decomposition allows an expansion of the Tutte polynomial of matroid perspective over cyclic flats. This can be used to speed up the computation of various evaluations of the polynomial.

Journal Article Type Article
Publication Date Jun 6, 2016
Journal Discrete Mathematics
Print ISSN 0012-365X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 339
Issue 6
Pages 1629-1639
APA6 Citation Kayibi, K. K., & Pirzada, S. (2016). On the activities of p-basis of matroid perspectives. Discrete Mathematics, 339(6), 1629-1639. doi:10.1016/j.disc.2016.01.013
DOI https://doi.org/10.1016/j.disc.2016.01.013
Publisher URL https://www.sciencedirect.com/science/article/pii/S0012365X16000236?via%3Dihub
Additional Information This article is maintained by: Elsevier; Article Title: On the activities of -basis of matroid perspectives; Journal Title: Discrete Mathematics; CrossRef DOI link to publisher maintained version: http://dx.doi.org/10.1016/j.disc.2016.01.013; Content Type: article; Copyright: Copyright © 2016 Elsevier B.V. All rights reserved.


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