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 theoreticalcomputer 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 and theoretical physics. 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 toresearch 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 and theoretical physics. 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 and theoretical physics. The main results in the field are collected in this up-to-date, comprehensive reference volumeThe author addresses differences in ideas and notations, highlights the main achievements, and points to research directions and open problemsWill be of interest to researchers and graduate students in theoretical computer science and mathematics INDICE: Simple Permutations and Permutation Patterns. Bijections Between Restricted Permutations and Other Combinatorial Objects. A 30-Year History of Bijections Between 321- and 132-Avoiding Permutations. What Do We Know About Stack-Sortable Permutations?- Chebyshev Polynomials in Connection with Patterns in Permutations. Consecutive Patterns in Permutations. Patterns in Combinatorics on Words. Packing Density for Sets of Patterns. On the (Former) Stanley—Wilf Conjecture. Properties of Permutations and Words Avoiding the Pattern 132. On Permutations Containing Many Different Patterns. ECO Method for Restricted Permutations. Symmetric Functions in Connection with Patterns in Permutations and Words. Counting Occurrences of Patterns in Finite Approximations of CertainInfinite Ssequences. On Classes of Wilf-Equivalent Permutation Patterns. WhatIs a Generalized Pattern?. References.
- ISBN: 978-3-642-17332-5
- Editorial: Springer Berlin Heidelberg
- Encuadernacion: Cartoné
- Páginas: 450
- Fecha Publicación: 15/07/2011
- Nº Volúmenes: 1
- Idioma: Inglés