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In mathematics, the permutohedron of order n is an (n − 1)-dimensional polytope embedded in an n-dimensional space. Its vertex coordinates (labels) are the permutations of the first n natural numbers. The edges identify the shortest possible paths (sets of transpositions) that connect two vertices (permutations). Two permutations connected by an edge differ in only two places (one transposition), and the numbers on these places are neighbors (differ in value by 1).

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  • Permutaeder (de)
  • Permuta hiperpluredro (eo)
  • Permutohedron (en)
  • Перестановочный многогранник (ru)
rdfs:comment
  • En matematiko, la permuta hiperpluredro de ordo n estas (n − 1)-dimensia hiperpluredro enigita en n-dimensia spaco, koordinatoj de verticoj de kiu estas formitaj per permutado de la vektoro (1, 2, 3, ..., n). La permuta hiperpluredro de ordo n estas ankaŭ la (n − 1)-simplaĵo. (eo)
  • Ein Permutaeder ist in der Mathematik ein konvexes Polytop (verallgemeinertes Vieleck) im -dimensionalen Raum, dessen Ecken durch die Permutationen der Koordinaten des Vektors entstehen. (de)
  • В математике перестановочный многогранник порядка n — это (n − 1)-мерный выпуклый многогранник, вложенный в n-мерное евклидово пространство, который является выпуклой оболочкой всех n! точек, получающихся перестановками координат вектора (1, 2, 3, …, n). (ru)
  • In mathematics, the permutohedron of order n is an (n − 1)-dimensional polytope embedded in an n-dimensional space. Its vertex coordinates (labels) are the permutations of the first n natural numbers. The edges identify the shortest possible paths (sets of transpositions) that connect two vertices (permutations). Two permutations connected by an edge differ in only two places (one transposition), and the numbers on these places are neighbors (differ in value by 1). (en)
foaf:depiction
  • http://commons.wikimedia.org/wiki/Special:FilePath/Hexagonal_tiling.svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Omnitruncated_Hexateron_as_Permutohedron.svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Permutohedron_3_subsets_1_(first).svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Permutohedron_3_subsets_2_(first).svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Permutohedron_4_subsets_1_(first).svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Permutohedron_4_subsets_2_(first).svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Permutohedron_4_subsets_3_(first).svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Permutohedron_order_2.svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Symmetric_group_4;_Cayley_graph_1,2,6_(1-based).png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Symmetric_group_4;_permutohedron_3D;_transpositions_(1-based).png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Weak_orderings_3_Hasse.svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Weak_orderings_4_Hasse.svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Bitruncated_cubic_honeycomb.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Permutohedron.svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Permutohedron_order_3.svg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Omnitruncated_5Cell_as_Permutohedron.svg
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