Abstract
Given a family A of subsets of an ordered set E, we define a construction giving a family of sets B in 1–1 correspondence with A; the same construction applied to B then gives A. For each subset X of E, \(A \cap B \subseteq X \subseteq A \cup B\) for exactly one pair of A∈A and corresponding B∈B. When the family B is the basis collection of a matroid on E, A can be described simply in terms of the matroid structure. A polynomial is defined which, in this latter case, is the Tutte polynomial of the matroid.
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References
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© 1981 Springer-Verlag
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Dawson, J.E. (1981). A construction for a family of sets and its application to matroids. In: McAvaney, K.L. (eds) Combinatorial Mathematics VIII. Lecture Notes in Mathematics, vol 884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091815
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DOI: https://doi.org/10.1007/BFb0091815
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