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 KazhdanLusztig 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.

The main results in the field are collected in this up-to-date, comprehensive reference volume The author addresses differences in ideas and notations, highlights the main achievements, and points to research directions and open problems Will be of interest to researchers and graduate students in theoretical computer science and mathematics Includes supplementary material: sn.pub/extras

Autorentext

Dr. Sergey Kitaev is a Reader in Combinatorics in the Department of Computer and Information Sciences of the University of Strathclyde. He studied at Novosibirsk State University, specializing in mathematical cybernetics, and received his Ph.D. from the University of Gothenburg in 2003. He has held visiting positions at the University of California, San Diego, the Sobolev Institute of Mathematics, and the Royal Swedish Academy of Sciences, and most recently he was an Associate Professor of Mathematics in Reykjavik University. He authored the (Springer) monograph "Patterns in Permutations and Words" in 2011. His research focuses on combinatorics, discrete analysis, graph theory, and formal languages. Prof. Vadim Lozin is a Professor in the Mathematics Institute at the University of Warwick. He received his Ph.D. in theoretical informatics from the University of Nizhny Novgorod in 1995. He was a visiting professor at Rutgers University, and he has held academic and visiting positions in Russia, Sweden, Switerland, Portugal, Germany, Canada, Saudi Arabia and France. He is the Managing Editor of the (Elsevier) Electronic Notes in Discrete Mathematics, and an Associate Editor of the (Elsevier) journal Discrete Applied Mathematics. His research focuses on graph theory, combinatorics, and discrete mathematics.

Inhalt

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.