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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 1999

A characterization for all interval doubling schemes of the lattice of permutations

Abstract

The lattice \textbfS_n of all permutations on a n-element set has been shown to be \emphbounded [CAS], which is a strong constructive property characterized by the fact that \textbfS_n admits what we call an \emph interval doubling scheme. In this paper we characterize all interval doubling schemes of the lattice \textbfS_n, a result that gives a nice precision on the bounded nature of the lattice of permutations. This theorem is a direct corollary of two strong properties that are also given with their proofs.
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Dates and versions

hal-00958936 , version 1 (13-03-2014)

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Nathalie Caspard. A characterization for all interval doubling schemes of the lattice of permutations. Discrete Mathematics and Theoretical Computer Science, 1999, Vol. 3 no. 4 (4), pp.177-188. ⟨10.46298/dmtcs.264⟩. ⟨hal-00958936⟩
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