The diagram of the permutohedron lattice is the intersection of the diagrams of two direct products of linear orders. (Le diagramme du treillis permutoèdre 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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