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permutohedron
In mathematics, the permutohedron of order ''n'' (also spelled permutahedron)〔.〕 is an (''n'' − 1)-dimensional polytope embedded in an ''n''-dimensional space, the vertices of which are formed by permuting the coordinates of the vector (1, 2, 3, ..., ''n'').
==History==
According to , permutohedra were first studied by . The name "permutohedron" (or rather its French version, "permutoèdre") was coined by . Regarding this coinage, they write that the word "permutohedron" is barbaric, but easy to remember, and that they submit it to the criticism of their readers.〔Original French: "le mot permutoèdre est barbare, mais il est facile à retenir; soumettons le aux critiques des lecteurs."〕
The alternative spelling permutahedron is sometimes also used. Permutohedra are sometimes also called permutation polytopes, but this terminology is also used for a related polytope, the Birkhoff polytope, defined as the convex hull of permutation matrices. More generally, uses the phrase "permutation polytope" for any polytope whose vertices are in 1-1 correspondence with the permutations of some set.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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