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Meet-distributive lattices and the anti-exchange closure

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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.

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Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Paul H. Edelman

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  1. Paul H. Edelman
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Work done while the author was an Applied Mathematics Fellow at M.I.T.

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Edelman, P.H. Meet-distributive lattices and the anti-exchange closure. Algebra Universalis 10, 290–299 (1980). https://doi.org/10.1007/BF02482912

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  • DOI: https://doi.org/10.1007/BF02482912

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