File:Symmetric group 4; permutohedra; transposition edges.svg
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Size of this PNG preview of this SVG file: 434 × 600 pixels. Other resolutions: 174 × 240 pixels | 347 × 480 pixels | 556 × 768 pixels | 741 × 1,024 pixels | 1,482 × 2,048 pixels | 744 × 1,028 pixels.
Original file (SVG file, nominally 744 × 1,028 pixels, file size: 844 KB)
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Summary
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The edges in the permutohedron of the symmetric group S4 correspond to transpositions. When two permutations are linked by a highlighted edge, representing one of six transpositions, this transposition turns one permutation into the other and vice versa. E.g. in the top permutohedron the permutations p3 and p5 are linked by a highlighted edge, representing transposition p2. (enlarge) So p3*p2=p5 and p5*p2=p3. See Cayley table: |
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 23:18, 2 March 2011 | | 744 × 1,028 (844 KB) | Watchduck | backwards notation (transposed matrix) |
| 20:21, 25 August 2010 |  | 744 × 1,028 (995 KB) | Watchduck |
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