On a generalization of spikes

Nick Brettell, Rutger Campbell, Deborah Chun, Kevin Grace, Geoff Whittle

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Samenvatting

We consider matroids with the property that every subset of the ground set of size t is contained in both an ℓ-element circuit and an ℓ-element cocircuit; we say that such a matroid has the (t, ℓ)-property. We show that for any positive integer t, there is a finite number of matroids with the (t, ℓ)-property for ℓ < 2t; however, matroids with the (t, 2t)-property form an infinite family. We say a matroid is a t-spike if there is a partition of the ground set into pairs such that the union of any t pairs is a circuit and a cocircuit. Our main result is that if a sufficiently large matroid has the (t, 2t)-property, then it is a t-spike. Finally, we present some properties of t-spikes.

Originele taal-2Engels
Pagina's (van-tot)358-372
Aantal pagina's15
TijdschriftSIAM Journal on Discrete Mathematics
Volume33
Nummer van het tijdschrift1
DOI's
StatusGepubliceerd - 1 jan 2019

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  • Citeer dit

    Brettell, N., Campbell, R., Chun, D., Grace, K., & Whittle, G. (2019). On a generalization of spikes. SIAM Journal on Discrete Mathematics, 33(1), 358-372. https://doi.org/10.1137/18M1182255