Nathalie Caspard - A characterization for all interval doubling schemes of the lattice of permutations

dmtcs:264 - Discrete Mathematics & Theoretical Computer Science, January 1, 1999, Vol. 3 no. 4 - https://doi.org/10.46298/dmtcs.264
A characterization for all interval doubling schemes of the lattice of permutationsArticle

Authors: Nathalie Caspard 1

  • 1 CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique

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.


Volume: Vol. 3 no. 4
Published on: January 1, 1999
Imported on: March 26, 2015
Keywords: Permutations,lattice,bounded lattice,interval doubling schemes,arrow relations,linear extension,tableaux,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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