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Title: | Orienting transversals and transition polynomials of multimatroids | Authors: | BRIJDER, Robert | Issue Date: | 2018 | Source: | ADVANCES IN APPLIED MATHEMATICS, 94, p. 120-155 | Abstract: | Multimatroids generalize matroids, delta-matroids, and isotropic systems, and transition polynomials of multimatroids subsume various polynomials for these latter combinatorial structures, such as the interlace polynomial and the Tutte-Martin polynomial. We prove evaluations of the Tutte-Martin polynomial of isotropic systems from Bouchet directly and more efficiently in the context of transition polynomials of multimatroids. Moreover, we generalize some related evaluations of the transition polynomial of 4-regular graphs from Jaeger to multimatroids. These evaluations are obtained in a uniform and matroid-theoretic way. We also translate the evaluations in terms of the interlace polynomial of graphs. Finally, we give an excluded-minor theorem for the class of binary tight 3-matroids (a subclass of multimatroids) based on the excluded-minor theorem for the class of binary delta-matroids from Bouchet. (C) 2017 Elsevier Inc. All rights reserved. | Notes: | Brijder, R (reprint author), Hasselt Univ, Hasselt, Belgium. robert.brijder@uhasselt.be | Keywords: | multimatroid; isotropic system; transition polynomial; tutte polynomial; interlace polynomial; matroid; 4-Regular graph | Document URI: | http://hdl.handle.net/1942/26415 | ISSN: | 0196-8858 | e-ISSN: | 1090-2074 | DOI: | 10.1016/j.aam.2017.07.001 | ISI #: | 000423887200007 | Rights: | © 2017 Elsevier Inc. All rights reserved. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2019 |
Appears in Collections: | Research publications |
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brijder 1.pdf Restricted Access | Published version | 389.9 kB | Adobe PDF | View/Open Request a copy |
bin_mm_pol_div2.pdf | Non Peer-reviewed author version | 506.25 kB | Adobe PDF | View/Open |
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