algebra universalis

, Volume 10, Issue 1, pp 290–299 | Cite as

Meet-distributive lattices and the anti-exchange closure

  • Paul H. Edelman


This paper defines the anti-exchange closure, a generalization of the order ideals of a partially ordered set. Various theorems are proved about this closure. The main theorem presented is that a latticeL is the lattice of closed sets of an anti-exchange closure if and only if it is a meet-distributive lattice. This result is used to give a combinatorial interpretation of the zetapolynomial of a meet-distributive lattice.


Boolean Algebra Distributive Lattice Algebra UNIV Order Ideal Boolean Lattice 
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Copyright information

© Birkhäuser Verlag 1980

Authors and Affiliations

  • Paul H. Edelman
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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