Details of Grant 

EPSRC Reference:	EP/J006440/1
Title:	The Structure of Permutation Classes
Principal Investigator:	Ruskuc, Professor N
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics and Statistics
Organisation:	University of St Andrews
Scheme:	Standard Research
Starts:	21 October 2011	Ends:	20 October 2014	Value (£):	66,715
EPSRC Research Topic Classifications:	Logic & Combinatorics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 05 Sep 2011 Mathematics Prioritisation Panel Meeting September 2011 Announced
Summary on Grant Application Form
Permutations are among most fundamental and ubiquitous abstract mathematical concepts, and are indispensable in modeling a vast array of higher level phenomena in other sciences: from the study of symmetries of the material world in Physics, via genome rearrangements and evolution in Biology to the study of data processing in Computer Science. In many of these, the order-theoretic properties of permutations are of chief importance, and the abstract theory underlying this facet is known as the theory of permutation patterns. From its beginnings as a small topic in Knuth's Art of Computer Programming to do with stack sorting, the theory has undergone a period of rapid expansion and development over the past two decades. The PI and his two proposed collaborators Albert and Vatter have made several ground breaking contributions to this development, consistently placing emphasis on the theoretical/structural foundations of the field, on the links with other parts of mathematics, and on general applicability. This effort has, in the past year, lead the team to the realisation of the crucial importance of so called grid decompositions, and associated geometric ways of representing pattern classes. There is strong evidence that this, combined with the existing theory of encodings by words and formal languages, will provide both a comprehensive structure theory for pattern classes and a pathway to solving several outstanding open problems.
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Organisation Website:	http://www.st-and.ac.uk