Patroids |
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| Authors: | Cedric AB Smith |
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| Institution: | Galton Laboratory, University College London, London NW1 2HE, England |
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| Abstract: | A matroid M over a set E of elements is semiseparated by a partition {S1, S2} of E iff rank E = rank S1 + rank S2 + 1. Such a semiseparation defines in each Si a pair of matroids or patroid Pi = (Mi, mi); the two patroids P1, P2 weld to form M. The operations of removing and contracting a non-degenerate element of a matroid produce a patroid. The properties of patroids, their bases, and circuits are discussed. |
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