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Algorithmic combinatorics on partial words

Author: Francine Blanchet-Sadri
Publisher: Boca Raton, FL : Chapman & Hall/CRC, ©2008.
Series: Discrete mathematics and its applications.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"This five-part book begins with a section on basics that covers terminology, the compatibility of partial words, and combinatorial properties of words. The book then focuses on three important concepts of periodicity on partial words: period, weak period, and local period. The next part describes a linear time algorithm to test primitivity on partial words and extends the results on unbordered words to unbordered  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Francine Blanchet-Sadri
ISBN: 9781420060928 1420060929
OCLC Number: 148877230
Description: 385 pages : illustrations ; 25 cm.
Contents: I. Basics --
1. Preliminaries on Partial Words --
1.1. Alphabets, letters, and words --
1.2. Partial functions and partial words --
1.3. Periodicity --
1.4. Factorizations of partial words --
1.5. Recursion and induction on partial words --
1.6. Containment and compatibility --
2. Combinatorial Properties of Partial Words --
2.1. Conjugacy --
2.2. Commutativity --
II. Periodicity --
3. Fine and Wilf's Theorem --
3.1. Case of zero or one hole --
3.2. Case of two or three holes --
3.3. Special partial words --
3.4. Graphs associated with partial words --
3.5. Main result --
3.6. Related results --
4. Critical Factorization Theorem --
4.1. Orderings --
4.2. Zero-hole case --
4.3. Main result: First version --
4.4. Main result: second version --
4.5. Tests --
5. Guibas and Odlyzko's Theorem --
5.1. Zero-hole case --
5.2. Main result --
5.3. Algorithm --
III. Primitivity --
6. Primitive partial words --
6.1. Testing primitivity on partial words --
6.2. Counting primitive partial words --
6.3. Exact periods --
6.4. First counting method --
6.5. Second counting method --
6.6. Existence of primitive partial words --
7. Unbordered Partial Words --
7.1. Concatenations of prefixes --
7.2. More results on concatenations of prefixes --
7.3. Critical factorizations --
7.4. Conjugates --
IV. Coding --
8. Pcodes of partial words --
8.1. Binary relations --
8.2. Pcodes --
8.3. Pcodes and monoids --
8.4. Prefix and suffix orderings --
8.5. Border ordering --
8.6. Commutative ordering --
8.7. Circular pcodes --
9. Deciding the Pcode Property --
9.1. First algorithm --
9.2. Second algorithm --
V. Further Topics --
10. Equations on Partial Words --
10.1. Equation x[superscript m] [actual symbol not reproducible] y[superscript n] --
10.2. Equation x[superscript 2] [actual symbol not reproducible] y[superscript m]z --
10.3. Equation x[superscript m]y[superscript n] [actual symbol not reproducible] z[superscript p] --
11. Correlations of Partial Words --
11.1. Binary and ternary correlations --
11.2. Characterizations of correlations --
11.3. Distributive lattices --
11.4. Irreducible period sets --
11.5. Counting correlations Exercises --
12. Unavoidable Sets of Partial Words --
12.1. Unavoidable sets --
12.2. Classifying unavoidable sets of size two --
12.3. case where k = 1 and l = 1 --
12.4. case where k = 1 and l = 2 --
12.5. Larger values of k and l.
Series Title: Discrete mathematics and its applications.
Responsibility: Francine Blanchet-Sadri.
More information:

Abstract:

Presents a mathematical treatment of combinatorics on partial words designed around algorithms and explores the techniques for solving partial word problems. This book provides algorithms in English  Read more...

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