<abstract xmlns="http://www.w3.org/1999/xhtml">Let T(M; x,y) = ∑ij Tij xiyjdenote the Tutte polynomial of the matroid M. If Tij is a corner of T (M; x, y), then Tij counts the sets of corank i and nullity j and each such set is a cyclic flat of M. The main result of this article consists of extending the definition of cyclic flats to a pair of matroids and proving that the corners of the linking polynomial give the lower bound of the number of the cyclic flats of the matroid pair.</abstract>

Let T(M; x,y) = ∑ij Tij xiyjdenote the Tutte polynomial of the matroid M. If Tij is a corner of T (M; x, y), then Tij counts the sets of corank i and nullity j and each such set is a cyclic flat of M. The main result of this article consists of extending the definition of cyclic flats to a pair of matroids and proving that the corners of the linking polynomial give the lower bound of the number of the cyclic flats of the matroid pair.

Cyclic flats and corners of the linking polynomial

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Cyclic flats and corners of the linking polynomial"}

Let T(M; x,y) = ∑ij Tij xiyjdenote the Tutte polynomial of the matroid M. If Tij is a corner of T (M; x, y), then Tij counts the sets of corank i and nullity j...

Cyclic flats and corners of the linking polynomial

Publié en ligne: 10 sept. 2018

Pages: 189 - 197

Reçu: 10 déc. 2017

DOI: https://doi.org/10.2478/ausm-2018-0016

Mots clés
matroid, cyclic flat, Tutte polynomial, linking polynomial

© 2018 Koko K. Kayibi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Cyclic flats and corners of the linking polynomial

Publié en ligne: 10 sept. 2018

Pages: 189 - 197

Reçu: 10 déc. 2017

DOI: https://doi.org/10.2478/ausm-2018-0016

Mots clésmatroid, cyclic flat, Tutte polynomial, linking polynomial

© 2018 Koko K. Kayibi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
matroid, cyclic flat, Tutte polynomial, linking polynomial