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Enumeration of permutations with forbidden templates.
- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Zhang, Yuang-Sheng.
- Language:
- English
- Subjects (All):
- Mathematics.
- 0405.
- Penn dissertations--Mathematics.
- Mathematics--Penn dissertations.
- Local Subjects:
- Penn dissertations--Mathematics.
- Mathematics--Penn dissertations.
- 0405.
- Physical Description:
- 88 pages
- Contained In:
- Dissertation Abstracts International 62-02B.
- System Details:
- Mode of access: World Wide Web.
- text file
- Summary:
- For any permutation sigma of k letters, a permutation pi avoids sigma iff there is no number i with 0 < i < n - 1 such that [pi(i), pi( i + 1), &cdots; , pi(i + k - 1)] is order-isomorphic to [sigma(1), sigma(2), &cdots; , sigma(k)]. In other words, there is no continuous subsequence of pi of length k such that it has the same pairwise comparisons of letters as sigma. We will call sigma a template and A(sigma, n) will be the number of permutations in Sn which forbids the template sigma. We find the cardinality of A(sigma, n) for various sigma as well as for some sets of sigma's. We also establish the recurrence structure of A(sigma, n) and find the upper bound and lower bound of A(sigma, n) for sigma with a certain length.
- Notes:
- Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 2001.
- Source: Dissertation Abstracts International, Volume: 62-02, Section: B, page: 0894.
- Supervisor: Herbert S. Wilf.
- Local Notes:
- School code: 0175.
- ISBN:
- 9780493134703
- Access Restriction:
- Restricted for use by site license.
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