Classes of Matroids Closed Under Minors and Principal Extensions

0506896 - ÚTIA 2020 RIV HU eng J - Journal Article
Matúš, František
Classes of Matroids Closed Under Minors and Principal Extensions.
Combinatorica. Roč. 38, č. 4 (2018), s. 935-954. ISSN 0209-9683. E-ISSN 1439-6912
R&D Projects: GA ČR GA13-20012S
Institutional support: RVO:67985556
Keywords : Matroids * Measures of information * Coding theorems
OECD category: Pure mathematics
Impact factor: 1.143, year: 2018
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2019/MTR/matus-0506896.pdf https://link.springer.com/article/10.1007/s00493-017-3534-y

This work studies the classes of matroids that are closed under minors, addition of coloops and principal extensions. To any matroid M in such a class a matroid M° is constructed such that it contains M as a minor, has all proper minors in the class and violates Zhang- Yeung inequality. When the class enjoys the inequality the matroid M° becomes an excluded minor. An analogous assertion was known before for the linear matroids over any infinite field in connection with Ingleton inequality. The result is applied to the classes of multilinear, algebraic and almost entropic matroids. In particular, the class of almost entropic matroids has infinitely many excluded minors.
Permanent Link: http://hdl.handle.net/11104/0298024