Lexicographic ordering of an n-element set / Danna Joy S. Ramonal
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TextLanguage: English Publication details: 2002Description: 22 leavesSubject(s): Dissertation note: Thesis (BS Applied Mathematics) -- University of the Philippines Mindanao, 2002 Abstract: Consider all the possible permutations of an n-element set {1,2,..,n} taken k at a time. Suppose these permutations arranged in lexicographic order. How do you determine the rank or position of a given permutation in the list? How do you find the particular permutation given its rank or position? This paper gives a formula for determining the rank or position of a permutation in the list and a formula for obtaining the particular permutation of a given rank or position, for n ranging from 1 to 9, without actually listing all the permutations involved. The lists of permutations is lexicographic order were observed for similar patterns that led to generate the formula. Would it be possible to generate a formula in finding the rank or position of the permutation and the permutation of the position if a certain number in the set of n elements is chosen and allow it to repeat n times? Would it also be possible to generate a formula in finding the rank or position of the permutation and the permutation of the position if a certain number in the set of n elements is chosen to have a fixed repetition?
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University Library Theses | Room-Use Only | LG993.5 2002 A64 R356 (Browse shelf(Opens below)) | Not For Loan | 3UPML00010961 | |
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Thesis
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University Library Archives and Records | Preservation Copy | LG993.5 2002 A64 R356 (Browse shelf(Opens below)) | Not For Loan | 3UPML00020911 |
Thesis (BS Applied Mathematics) -- University of the Philippines Mindanao, 2002
Consider all the possible permutations of an n-element set {1,2,..,n} taken k at a time. Suppose these permutations arranged in lexicographic order. How do you determine the rank or position of a given permutation in the list? How do you find the particular permutation given its rank or position? This paper gives a formula for determining the rank or position of a permutation in the list and a formula for obtaining the particular permutation of a given rank or position, for n ranging from 1 to 9, without actually listing all the permutations involved. The lists of permutations is lexicographic order were observed for similar patterns that led to generate the formula. Would it be possible to generate a formula in finding the rank or position of the permutation and the permutation of the position if a certain number in the set of n elements is chosen and allow it to repeat n times? Would it also be possible to generate a formula in finding the rank or position of the permutation and the permutation of the position if a certain number in the set of n elements is chosen to have a fixed repetition?
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