Permutation Patterns

The study of permutation patterns is a thriving area of combinatorics that relates to many other areas of mathematics, including graph theory, enumerative combinatorics, model theory, the theory of automata and languages, and bioinformatics. Arising from the Fifth International Conference on Permutation Patterns, held in St Andrews in June 2007, this volume contains a mixture of survey and research articles by leading experts, and includes the two invited speakers, Martin Klazar and Mike Atkinson. Together, the collected articles cover all the significant strands of current research: structural methods and simple patterns, generalisations of patterns, various enumerative aspects, machines and networks, packing, and more. Specialists in this area and other researchers in combinatorics and related fields will find much of interest in this book. In addition, the volume provides plenty of material accessible to advanced undergraduates and is a suitable reference for projects and dissertations.

Preface	p. 1
Some general results in combinatorial enumeration	p. 3
A survey of simple permutations	p. 41
Permuting machines and permutation patterns	p. 67
On three different notions of monotone subsequences	p. 89
A survey on partially ordered patterns	p. 115
Generalized permutation patterns - a short survey	p. 137
An introduction to structural methods in permutation patterns	p. 153
Combinatorial properties of permutation tableaux	p. 171
Enumeration schemes for words avoiding permutations	p. 193
The lexicographic first occurrence of a I-II-III-pattern	p. 213
Enumeration of partitions by rises, levels and descents	p. 221
Restricted patience sorting and barred pattern avoidance	p. 233
Permutations with k-regular descent patterns	p. 259
Packing rates of measures and a conjecture for the packing density of 2413	p. 287
On the permutational power of token passing networks	p. 317
Problems and conjectures	p. 339
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