Classes of Matroids Closed Under Minors and Principal Extensions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00506896" target="_blank" >RIV/67985556:_____/18:00506896 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00493-017-3534-y" target="_blank" >https://link.springer.com/article/10.1007/s00493-017-3534-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00493-017-3534-y" target="_blank" >10.1007/s00493-017-3534-y</a>

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
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA13-20012S" target="_blank" >GA13-20012S: Conditional independence structures: algebraic and geometric methods</a><br>
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

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