The visually distinct configurations of k sets |
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Authors: | James F Lynch |
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Institution: | Department of Mathematics and Computer Science, Clarkson College, Potsdam, NY 13676, USA |
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Abstract: | Two sets of sets, C0 and C1, are said to be visually equivalent if there is a 1-1 mapping m from C0 onto C1 such that for every S, T?C0, S ∩ T=0 if and only if m(S)∩ m(T)=0 and S?T if and only if m(S)?m(T). We find estimates for V(k), the number of equivalence classes of this relation on sets of k sets, for finite and infinite k. Our main results are that for finite k, , where α and β are approximately 0.7255 and 2.5323 respectively, and there is a set N of cardinality such that there are V(k) visually distinct sets of k subsets of N. |
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