On the number of circuit-cocircuit reversal classes of an oriented matroid

Gioan, Emeric; Yuen, Chi Ho (2019). On the number of circuit-cocircuit reversal classes of an oriented matroid. Discrete mathematics, 342(4), pp. 1056-1059. Elsevier 10.1016/j.disc.2018.12.006

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The first author introduced the circuit–cocircuit reversal system of an oriented matroid, and showed that when the underlying matroid is regular, the cardinalities of such system and its variations are equal to special evaluations of the Tutte polynomial (e.g., the total number of circuit–cocircuit reversal classes equals t(M;1,1), the number of bases of the matroid). By relating these classes to activity classes studied by the first author and Las Vergnas, we give an alternative proof of the above results and a proof of the converse statements that these equalities fail whenever the underlying matroid is not regular. Hence we extend the above results to an equivalence of matroidal properties, thereby giving a new characterization of regular matroids.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Yuen, Chi Ho

Subjects:

500 Science > 510 Mathematics

ISSN:

0012-365X

Publisher:

Elsevier

Language:

English

Submitter:

Michel Arthur Bik

Date Deposited:

06 Aug 2019 14:22

Last Modified:

22 Oct 2019 17:31

Publisher DOI:

10.1016/j.disc.2018.12.006

BORIS DOI:

10.7892/boris.132262

URI:

https://boris.unibe.ch/id/eprint/132262

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