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Type B 的排列多面體 = On the Permutohedron...

國立高雄大學應用數學系碩士班

Type B 的排列多面體 = On the Permutohedron of type B

Record Type:	Language materials, printed : monographic
Paralel Title:	On the Permutohedron of type B
Author:	莊宛臻,
Secondary Intellectual Responsibility:	國立高雄大學
Place of Publication:	[高雄市]
Published:	撰者;
Year of Publication:	民99[2010]
Description:	47面圖，表 : 30公分;
Subject:	多面體
Subject:	permutohedron
Online resource:	http://handle.ncl.edu.tw/11296/ndltd/91999787683334154290
Summary:	在此篇論文中，我們將探討type B的排列多面體(PBn)的一些基本性質。我們證明出type B的兩個排列在PBn中是相鄰的二頂點若且為若此兩個排列的其中一個可由另一個經由 (1)保持正負號位置下交換數字i與i+1或 (2)改變數字1的正負號而得。我們也證明PBn可用3n-1個不等式的解刻劃出來。此外，我們求出PBn的f-vector與h-vector。最後證明PBn的1-skeleton有Hamiltonian環遊。為了完整起見，type A的結果亦一併呈現於論文中。 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.

Type B 的排列多面體 = On the Permutohedron of type B
莊, 宛臻

Type B 的排列多面體 = On the Permutohedron of type B / 莊宛臻撰 - [高雄市] : 撰者, 民99[2010]. - 47面 ; 圖，表 ; 30公分.
參考書目：面.
多面體permutohedron

Type B 的排列多面體 = On the Permutohedron of type B
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328 $a 碩士論文--國立高雄大學應用數學系碩士班
330 $a 在此篇論文中，我們將探討type B的排列多面體(PBn)的一些基本性質。我們證明出type B的兩個排列在PBn中是相鄰的二頂點若且為若此兩個排列的其中一個可由另一個經由 (1)保持正負號位置下交換數字i與i+1或 (2)改變數字1的正負號而得。我們也證明PBn可用3n-1個不等式的解刻劃出來。此外，我們求出PBn的f-vector與h-vector。最後證明PBn的1-skeleton有Hamiltonian環遊。為了完整起見，type A的結果亦一併呈現於論文中。 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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