Patterns in Permutations and Words

Voorkant
Springer Science & Business Media, 30 aug. 2011 - 494 pagina's
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There has been considerable interest recently in the subject of patterns in permutations and words, a new branch of combinatorics with its roots in the works of Rotem, Rogers, and Knuth in the 1970s. Consideration of the patterns in question has been extremely interesting from the combinatorial point of view, and it has proved to be a useful language in a variety of seemingly unrelated problems, including the theory of Kazhdan—Lusztig polynomials, singularities of Schubert varieties, interval orders, Chebyshev polynomials, models in statistical mechanics, and various sorting algorithms, including sorting stacks and sortable permutations.

The author collects the main results in the field in this up-to-date, comprehensive reference volume. He highlights significant achievements in the area, and points to research directions and open problems. The book will be of interest to researchers and graduate students in theoretical computer science and mathematics, in particular those working in algebraic combinatorics and combinatorics on words. It will also be of interest to specialists in other branches of mathematics, theoretical physics, and computational biology.

The author collects the main results in the field in this up-to-date, comprehensive reference volume. He highlights significant achievements in the area, and points to research directions and open problems. The book will be of interest to researchers and graduate students in theoretical computer science and mathematics, in particular those working in algebraic combinatorics and combinatorics on words. It will also be of interest to specialists in other branches of mathematics, theoretical physics, and computational biology.

 

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Inhoudsopgave

Chapter 1 What is a pattern in a permutation or a word?
1
Chapter 2 Why such patterns? A few motivation points
29
Chapter 3 More motivation points
81
Chapter 4 Bijections between 321 and 132avoiding permutations
141
Chapter 5 Consecutive patterns
164
Chapter 6 Classical patterns and POPs
223
Chapter 7 VPs BVPs and BPs
291
Chapter 8 Miscellaneous on patterns in permutations and words
316
Chapter 9 Extending research on patterns in permutations and words to other domains
361
Appendix A Useful notions and facts
387
Appendix B Some algebraic background
401
Bibliography
405
Index
465
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Over de auteur (2011)

The author is a Reader in the Department of Computer and Information Sciences at the University of Strathclyde; his main research interests are enumerative and algebraic combinatorics, combinatorics on words, discrete analysis, graph theory and formal languages.

Bibliografische gegevens