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Geometric grid classes and the substitution decomposition have both been shown to be fundamental in the understanding of the structure of permutation classes.
Ordering by divisibility in abstract algebras
1952
Earlier work this paper cites.
Well-quasi-ordering, the Tree Theorem, and Vazsonyi’s conjecture
1960
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On well-quasi-ordering finite trees
1963
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On free monoids partially ordered by embedding
1969
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Computing permutations with double-ended queues, parallel stacks and parallel queues
1973
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Critically indecomposable partially ordered sets, graphs, tournaments and other binary relational structures
1993
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The enumeration of permutations with a prescribed number of “forbidden” patterns
1996
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Finiteness theorems for graphs and posets obtained by compositions
1999
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Introduction to automata theory, languages, and computation
2001
Cited alongside, same era.
Regular closed sets of permutations
2003
Cited alongside, same era.
Excluded permutation matrices and the Stanley-Wilf conjecture
2004
Cited alongside, same era.
Simple permutations and pattern restricted permutations
2005
Cited alongside, same era.
Problems and conjectures presented at the Third International Conference on Permutation Patterns, University of Florida, March 7–11, 2005
2005
Cited alongside, same era.
Hereditary properties of ordered graphs
2006
Cited alongside, same era.
Simple permutations and algebraic generating functions
2008
Later among the works it cites.
Growing at a perfect speed
2009
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Analytic combinatorics
2009
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Overview of some general results in combinatorial enumeration
2010
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Permutation classes of every growth rate above
2010
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Subclasses of the separable permutations
2011
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Small permutation classes
2011
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2006
Cited alongside, same era.
Wreath products of permutation classes
2007
Cited alongside, same era.
Geometric grid classes of permutations
Cited in the paper.