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.
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; 1. Some general results in combinatorial enumeration Martin Klazar; 2. A survey of simple permutations Robert Brignall; 3. Permuting machines and permutation patterns Mike Atkinson; 4. On three different notions of monotone subsequences Miklós Bóna; 5. A survey on partially ordered patterns Sergey Kitaev; 6. Generalized permutation patterns - a short survey Einar Steingrímsson; 7. An introduction to structural methods in permutation patterns Michael Albert; 8. Combinatorial properties of permutation tableaux Alexander Burstein and Niklas Eriksen; 9. Enumeration schemes for words avoiding permutations Lara Pudwell; 10. The lexicographic first occurrence of a I-II-III pattern Torey Burton, Anant P. Godbole and Brett M. Kindle; 11. Enumeration of partitions by rises, levels and descents Toufik Mansour and Augustine O. Munagi; 12. Restricted patience sorting and barred pattern avoidance Alexander Burstein and Isaiah Lankham; 13. Permutations with k-regular descent patterns Anthony Mendes, Jeffrey B. Remmel and Amanda Riehl; 14. Packing rates of measures and a conjecture for the packing density of 2413 Cathleen Battiste Presutti and Walter Stromquist; 15. On the permutational power of token passing networks Michael Albert, Steve Linton and Nik Rŭskuc; 16. Problems and conjectures.
A collection of survey and research articles representing all the main strands of research in permutation patterns.
Steve Linton is a Professor of Computer Science at the University of St Andrews, Scotland, where he directs the Centre for Interdisciplinary Research in Computational Algebra. Nik Ruškuc is a Professor of Mathematics at the University of St Andrews, Scotland. Vincent Vatter is a John Wesley Young Instructor at Dartmouth College, New Hampshire.
"This well-written collection of research papers by international
experts in the field covers all of the significant strands of
current research, including structural methods and simple patterns,
generalizations of patterns, various enumerative aspects, machines,
and networks. I highly recommend this book to specialists and
researchers in combinatorics. It should be noted that a few of the
current problems in the field of permutation patterns are listed at
the end of the book, which makes it a good starting point for
future projects and dissertations."
Hamid R. Noori, Computing Reviews
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