Patterns in Permutations and Words

ISBN-13: 9783642269875 / Angielski / Miękka / 2013 / 494 str.

Sergey Kitaev

Opis

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.

Recenzje

From the reviews:

"This book summarizes recent developments in the rapidly growing field of patterns in permutations and words. ... The book is a compendium of a great number of recent papers about patterns in permutations and words. ... The book is a good summary of the current state of the subject. The bibliography at the end of the book is especially comprehensive, and very useful for the reader who wants to learn more about particular topics." (Sergi Elizalde, Mathematical Reviews, September, 2013)

"The book presents the state of the art of 'patterns in permutations and words', a topic that has recently attracted considerable interest among researchers in various fields of mathematics and computer science, but also in theoretical physics and computational biology. It contains a list of 816 references and is well suited as a handbook for the methods and results of this area." (K. Auinger, Monatshefte für Mathematik, Vol. 170 (2), May, 2013)

"The monograph provides probably a first comprehensive overview of a vivid area of pattern observations, forming itself a common tool for various fields of mathematics. Containing a list of 816 references to recent and older literature, it has a good chance to become a handbook and a useful guide to results and techniques in the area." (Anton Cerny, Zentralblatt MATH, Vol. 1257, 2013)

Spis treści

Chap. 1, What Is a Pattern in a Permutation or a Word?.-

Chap. 2, Why Such patterns? A Few Motivation Points.-

Chap. 3, More Motivation Points.-

Chap. 4, Bijections Between 321- and 132-Avoiding Permutations.-

Chap. 5, Consecutive Patterns.-

Chap. 6, Classical Patterns and POPs.-

Chap. 7, VPs, BVPs and BPs.-

Chap. 8, Miscellaneous on Patterns in Permutations and Words.-

Chap. 9, Extending Research on Patterns in Permutations and Words to Other Domains.-

App. A, Useful Notions and Facts.-

App. B, Some Algebraic Background.-

Bibliography.-

Index.

O autorze

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.

Blurb

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.