algebra universalis

, Volume 49, Issue 1, pp 13–33 | Cite as

Finite distributive lattices and the splitting property

  • Dwight Duffus
  • Bill Sands
Regular article


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.

2000 Mathematics Subject Classification: 06A07, 06D99.¶Key words and phrases: Distributive lattice, maximal antichain, splitting property, splitting number, grid. 


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Copyright information

© Birkhäuser Verlag Basel, 2003

Authors and Affiliations

  • Dwight Duffus
    • 1
  • Bill Sands
    • 2
  1. 1.Mathematics and Computer Science Department, Emory University, Atlanta, GA 30322, USA, e-mail: US
  2. 2.Mathematics and Statistics Department, The University of Calgary, Calgary T2N 1N4, Canada, e-mail: sands@math.ucalgary.caCA

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