On Matroids which have Precisely One Basis in Common

Dress A (1988)
European Journal of Combinatorics 9(2): 149-151.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
A theorem concerning matroids is proved which—specialized to representable matroids—implies that given a non-singular quadratic n × n-matrix A = (aij) and some k ∈ {1,..., n − 1} such that for any subset S ⊆ {1,..., n} of cardinality k different from {1,..., k}, the product det ((aij)i = 1,...,k; j ∈ S) · det ((aij)i = k + 1,..., n; j ∉ S) in the Laplace expansion of A with respect to the first k and the last n − k rows vanishes, there exists some i ∈ {k + 1,..., n} with a1i = a2i = ⋯ =aki = 0 or some i ∈ {1,..., k) with ak+1,i = ak + 2,i = ⋯ = ani = 0.
Erscheinungsjahr
1988
Zeitschriftentitel
European Journal of Combinatorics
Band
9
Ausgabe
2
Seite(n)
149-151
ISSN
0195-6698
Page URI
https://pub.uni-bielefeld.de/record/1654173

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Dress A. On Matroids which have Precisely One Basis in Common. European Journal of Combinatorics. 1988;9(2):149-151.
Dress, A. (1988). On Matroids which have Precisely One Basis in Common. European Journal of Combinatorics, 9(2), 149-151. https://doi.org/10.1016/S0195-6698(88)80039-8
Dress, A. (1988). On Matroids which have Precisely One Basis in Common. European Journal of Combinatorics 9, 149-151.
Dress, A., 1988. On Matroids which have Precisely One Basis in Common. European Journal of Combinatorics, 9(2), p 149-151.
A. Dress, “On Matroids which have Precisely One Basis in Common”, European Journal of Combinatorics, vol. 9, 1988, pp. 149-151.
Dress, A.: On Matroids which have Precisely One Basis in Common. European Journal of Combinatorics. 9, 149-151 (1988).
Dress, Andreas. “On Matroids which have Precisely One Basis in Common”. European Journal of Combinatorics 9.2 (1988): 149-151.

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