English

The lattice of closure relations of a poset

Combinatorics 2016-09-06 v1

Abstract

In this paper we show that the set of closure relations on a finite poset P 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). We also characterize the modular elements of this lattice and compute its characteristic polynomial.

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Cite

@article{arxiv.math/9409218,
  title  = {The lattice of closure relations of a poset},
  author = {Michael Hawrylycz and Victor Reiner},
  journal= {arXiv preprint arXiv:math/9409218},
  year   = {2016}
}

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8 pages