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algebra universalis

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

Meet-distributive lattices and the anti-exchange closure

  • Paul H. Edelman
Article

Abstract

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.

Keywords

Boolean Algebra Distributive Lattice Algebra UNIV Order Ideal Boolean Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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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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