On the Permutohedron of type B
碩士 === 國立高雄大學 === 應用數學系碩士班 === 98 === In this thesis we investigate PBn, permutohedron of type B, and obtain some basic properties. We prove that two permutations of type B are adjacent in PBn if and only if one of them can be obtained from the other by exchanging the positions of numbers i and i+1...
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| Format: | Others |
| Language: | en_US |
| Published: |
2010
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| Online Access: | http://ndltd.ncl.edu.tw/handle/ehuz3q |
| Summary: | 碩士 === 國立高雄大學 === 應用數學系碩士班 === 98 === In this thesis we investigate PBn, permutohedron of type B, and obtain some basic properties. We prove that two permutations of type B are adjacent in PBn if and only if one of them can be obtained from the other by exchanging the positions of numbers i and i+1 while keeping the sign unchanged, or by changing the sign of the number 1. We also characterize PBn as the solution of the system of 3n-1 inequalities and obtain the f-vector and h-vector. Finally we prove the Hamiltonicity of the 1-skeleton of PBn. Corresponding results on permutohedron of type A are also included for completeness’s sake.
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