Classes of Matroids Closed Under Minors and Principal Extensions

Result code in IS VaVaI

RIV/67985556:_____/18:00506896 - isvavai.cz

Result on the web

https://link.springer.com/article/10.1007/s00493-017-3534-y

DOI - Digital Object Identifier

10.1007/s00493-017-3534-y

Result language

angličtina

Original language name

Classes of Matroids Closed Under Minors and Principal Extensions

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

GA13-20012S: Conditional independence structures: algebraic and geometric methods

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Combinatorica

ISSN

0209-9683

e-ISSN

—

Volume of the periodical

38

Issue of the periodical within the volume

4

Country of publishing house

HU - HUNGARY

Number of pages

20

Pages from-to

935-954

UT code for WoS article

000443306900008

EID of the result in the Scopus database

2-s2.0-85052592985