algebra universalis

, Volume 10, Issue 1, pp 290-299

Meet-distributive lattices and the anti-exchange closure

  • Paul H. EdelmanAffiliated withMassachusetts Institute of Technology

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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.