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A matroid extension result

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Authors : Oxley, James G. (Author of the conference)
CIRM (Publisher )

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Abstract : 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 $L$.

Keywords : matroid extension; Vamos matroid

MSC Codes :
05B35 - Matroids, geometric lattices

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 01/10/2018
    Conference Date : 24/09/2018
    Subseries : Research talks
    arXiv category : Combinatorics
    Mathematical Area(s) : Combinatorics
    Format : MP4 (.mp4) - HD
    Video Time : 00:18:23
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2018-09-24_Oxley.mp4

Information on the Event

Event Title : Combinatorial geometries: matroids, oriented matroids and applications / Géométries combinatoires : matroïdes, matroïdes orientés et applications
Event Organizers : Gioan, Emeric ; Ramírez Alfonsín, Jorge Luis ; Recski, Andras
Dates : 24/09/2018 - 28/09/2018
Event Year : 2018
Event URL : https://conferences.cirm-math.fr/1859.html

Citation Data

DOI : 10.24350/CIRM.V.19449503
Cite this video as: Oxley, James G. (2018). A matroid extension result. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19449503
URI : http://dx.doi.org/10.24350/CIRM.V.19449503

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