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Finite distributive lattices and the splitting property

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Abstract.

We show that a finite distributive lattice has the splitting property - every maximal antichain splits into two parts so that the lattice is the union of the upset of one part and the downset of the other - if and only if it is a Boolean lattice or is one of three other lattices. We also introduce a measure of "how splitting" a finite distributive lattice is, and investigate it.

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Authors and Affiliations

  1. Mathematics and Computer Science Department, Emory University, Atlanta, GA 30322, USA, e-mail: dwight@mathcs.emory.edu , , , , , , US

    Dwight Duffus

  2. Mathematics and Statistics Department, The University of Calgary, Calgary T2N 1N4, Canada, e-mail: sands@math.ucalgary.ca, , , , , , CA

    Bill Sands

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  1. Dwight Duffus
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  2. Bill Sands
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Received June 13, 2001; accepted in final form July 1, 2002.

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Duffus, D., Sands, B. Finite distributive lattices and the splitting property. Algebra univers. 49, 13–33 (2003). https://doi.org/10.1007/s000120300001

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  • DOI: https://doi.org/10.1007/s000120300001

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