The lattice of closure relations on a poset |
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| Authors: | Michael Hawrylycz Victor Reiner |
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| Institution: | (1) Department of Mathematics, University of Minnesota, Minneapolis, Minnesota, USA;(2) Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Masachusetts, USA |
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| Abstract: | In this paper we show that the set of closure relations on a finite posetP forms a supersolvable lattice, as suggested by Rota. Furthermore this lattice is dually isomorphic to the lattice of closed sets in a convex geometry (in the sense of Edelman and Jamison EJ]). We also characterize the modular elements of this lattice (whenP has a greatest element) and compute its characteristic polynomial.Presented by R. W. Quackenbush. |
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