Counting formulas for glued lattices |
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Authors: | Klaus Reuter |
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Institution: | (1) Fachbereich Mathematik, Technische Hochschule Darmstadt, West Germany |
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Abstract: | A tolerance relation of a lattice L, i.e., a reflexive and symmetric relation of L which is compatible with join and meet, is called glued if covering blocks of have nonempty intersection. For a lattice L with a glued tolerance relation we prove a formula counting the number of elements of L with exactly k lower (upper) covers. Moreover, we prove similar formulas for incidence structures and graphs and we give a new proof of Dilworth's covering theorem. |
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Keywords: | 05A15 06B05 |
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