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The diagram of the permutohedron lattice is the intersection of the diagrams of two direct products of linear orders. (Le diagramme du treillis permuto√®dre est intersection des diagrammes de deux produits directs d’ordres totaux.) (French) Zbl 0788.06002

Summary: Two codes are used on the set of permutations or linear orders on an \(n\)- element set. To each of them a direct product of total orders of \(2,3,\dots,n\) elements is associated. It is shown that the diagram of the permutohedron lattice (or weak Bruhat order on the symmetric group \(S_ n\)) is the intersection of the diagrams of the two direct products of \(n- 1\) linear orders.

MSC:

06A05 Total orders
05A05 Permutations, words, matrices
20B30 Symmetric groups
06F15 Ordered groups
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