A matroid extension result | Vidéo | Carmin.tv

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A matroid extension result

By James G. Oxley

Appears in collection : Combinatorial geometries: matroids, oriented matroids and applications / Géométries combinatoires : matroïdes, matroïdes orientés et applications

Let $(A,B)$ be a $3$-separation in a matroid $M$. If $M$ is representable, then, in the underlying projective space, there is a line where the subspaces spanned by $A$ and $B$ meet, and $M$ can be extended by adding elements from this line. In general, Geelen, Gerards, and Whittle proved that $M$ can be extended by an independent set ${p,q}$ such that ${p,q}$ is in the closure of each of $A$ and $B$. In this extension, each of $p$ and $q$ is freely placed on the line $L$ spanned by ${p,q}$. This talk will discuss a result that gives necessary and sufficient conditions under which a fixed element can be placed on $L$.

Information about the video

Date of recording 24/09/2018
Date of publication 01/10/2018
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19449503
Cite this video Oxley, James G. (24/09/2018). A matroid extension result. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19449503
URL https://dx.doi.org/10.24350/CIRM.V.19449503

Domain(s)

Combinatorics

Bibliography

Oxley, J. (2018). A matroid extension result. <arXiv:1805.04960> - https://arxiv.org/abs/1805.04960

MSC codes

05B35 Matroids, geometric lattices

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