<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

Published Online: Sep 10, 2018

Page range: 189 - 197

Received: Dec 10, 2017

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

Keywords
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

Published Online: Sep 10, 2018

Page range: 189 - 197

Received: Dec 10, 2017

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

Keywordsmatroid, 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.

Keywords
matroid, cyclic flat, Tutte polynomial, linking polynomial