Permutation Patterns, St Andrews 2007

353 Pages·2010·1.7 MB·English

by  Steve Linton

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LondonMathematicalSocietyLectureNoteSeries:376
Permutation Patterns
St Andrews 2007
Editedby
STEVE LINTON
UniversityofStAndrews
NIK RUSˇ KUC
UniversityofStAndrews
VINCENT VATTER
DartmouthCollege
CAMBRIDGE UNIVERSITY PRESS
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São Paulo, Delhi, Dubai, Tokyo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
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Information on this title: www.cambridge.org/9780521728348
© Cambridge University Press 2010
This publication is in copyright. Subject to statutory exception and to the
provision of relevant collective licensing agreements, no reproduction of any part
may take place without the written permission of Cambridge University Press.
First published in print format 2010
ISBN-13 978-0-511-90182-9 eBook (NetLibrary)
ISBN-13 978-0-521-72834-8 Paperback
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accurate or appropriate.
Contents
Preface page 1
Some general results in combinatorial enumeration 3
Martin Klazar
A survey of simple permutations 41
Robert Brignall
Permuting machines and permutation patterns 67
Mike Atkinson
On three different notions of monotone subsequences 89
Miklo´s Bo´na
A survey on partially ordered patterns 115
Sergey Kitaev
Generalized permutation patterns — a short survey 137
Einar Steingr´ımsson
An introduction to structural methods in
permutation patterns 153
Michael Albert
Combinatorial properties of permutation tableaux 171
Alexander Burstein and Niklas Eriksen
Enumeration schemes for words avoiding permutations 193
Lara Pudwell
The lexicographic first occurrence of a I-II-III-pattern 213
Torey Burton, Anant P. Godbole and Brett M. Kindle
Enumeration of partitions by rises, levels and descents 221
Toufik Mansour and Augustine O. Munagi
Restricted patience sorting and barred pattern avoidance 233
Alexander Burstein and Isaiah Lankham
Permutations with k-regular descent patterns 259
Anthony Mendes, Jeffrey B. Remmel and Amanda Riehl
Packing rates of measures and a conjecture for the packing
density of 2413 287
Cathleen Battiste Presutti and Walter Stromquist
On the permutational power of token passing networks 317
Michael Albert, Steve Linton and Nik Ruˇskuc
Problems and conjectures 339

Preface
The Permutation Patterns 2007 conference was held 11–15 June 2007
at the University of St Andrews. This was the fifth Permutation Pat-
ternsconference;thepreviousconferenceswereheldatOtagoUniversity
(Dundein, New Zealand), Malaspina College (Vancouver Island, British
Columbia), the University of Florida (Gainesville, Florida), and Reyk-
jav´ık University (Reykjav´ık, Iceland). The organizing committee was
comprisedofMiklo´sB´ona,LynnHynd,SteveLinton,NikRuˇskuc,Einar
Steingr´ımsson, Vincent Vatter, and Julian West. A half-day excursion
was taken to Falls of Bruar, Blair Athol Castle and The Queen’s View
on Loch Tummel.
There were two invited talks:
• Mike Atkinson (Otago University, Dunedin, New Zealand), “Simple
permutations and wreath-closed pattern classes”.
• Martin Klazar (Charles University, Prague, Czech Republic), “Poly-
nomial counting”.
Therewere35participants,23talks,andaproblemsession(theprob-
lems from which are included at the end of these proceedings). All the
main strands of research in permutation patterns were represented, and
we hope this is reflected by the articles of these proceedings, especially
the eight surveys at the beginning. The conference was supported by
the EPSRC and Edinburgh Mathematical Society.
1