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Invertibility of the base Radon transform of a matroid

✍ Scribed by Anders Björner; Johan Karlander

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
512 KB
Volume
108
Category
Article
ISSN
0012-365X

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✦ Synopsis

BjGmer, A. and J. Karlander, Invertibility of the base Radon transform of a matroid, Discrete Mathematics 108 (1992) 139-147.

Let M be a matroid of rank r on n elements and let F be a field. Assume that either char F = 0 or char F > r. It is shown that the point-base incidence matrix of M has rank n -k + 1 over F, where k is the number of connected components. This implies that the Radon transform on the family of bases is invertible if and only if the matroid is connected.

If M is loop-free then the Radon transform on the family of m-element independent sets is invertible, for every O<m<r.

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