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SMALL PERMUTATION CLASSES
, 2007
"... We establish a phase transition for permutation classes (downsets of permutations under the permutation containment order): there is an algebraic number κ, approximately 2.20557, for which there are only countably many permutation classes of growth rate (StanleyWilf limit) less than κ but uncountab ..."
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Cited by 17 (2 self)
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We establish a phase transition for permutation classes (downsets of permutations under the permutation containment order): there is an algebraic number κ, approximately 2.20557, for which there are only countably many permutation classes of growth rate (StanleyWilf limit) less than κ
Wreath Products of Permutation Classes
"... A permutation class which is closed under pattern involvement may be described in terms of its basis. The wreath product construction X ≀ Y of two permutation classes X and Y is also closed, and we exhibit a family of classes Y with the property that, for any finitely based class X, the wreath produ ..."
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Cited by 5 (0 self)
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A permutation class which is closed under pattern involvement may be described in terms of its basis. The wreath product construction X ≀ Y of two permutation classes X and Y is also closed, and we exhibit a family of classes Y with the property that, for any finitely based class X, the wreath
Combinatorial specification of permutation classes †
"... Abstract. This article presents a methodology that automatically derives a combinatorial specification for the permutation class C = Av(B), given its basis B of excluded patterns and the set of simple permutations in C, when these sets are both finite. This is achieved considering both pattern avoid ..."
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Cited by 3 (0 self)
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Abstract. This article presents a methodology that automatically derives a combinatorial specification for the permutation class C = Av(B), given its basis B of excluded patterns and the set of simple permutations in C, when these sets are both finite. This is achieved considering both pattern
The permutation classes equinumerous to the Smooth class
 J. Combin
, 1998
"... We determine all permutation classes defined by pattern avoidance which are equinumerous to the class of permutations whose Schubert variety is smooth. We also provide a lattice path interpretation for the numbers of such permutations. 1 Introduction Let q =(q 1 ,q 2 ,...,q k ) # S k be a permut ..."
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Cited by 40 (0 self)
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We determine all permutation classes defined by pattern avoidance which are equinumerous to the class of permutations whose Schubert variety is smooth. We also provide a lattice path interpretation for the numbers of such permutations. 1 Introduction Let q =(q 1 ,q 2 ,...,q k ) # S k be a
Permutation classes of polynomial growth
 Annals of Combinatorics
, 2007
"... A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and sufficient conditions on sets of forbidden permutations which ..."
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Cited by 8 (0 self)
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A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and sufficient conditions on sets of forbidden permutations
Approximations to permutation classes
, 2008
"... We investigate a new notion of approximately avoiding a permutation: π almost avoids β if one can remove a single entry from π to obtain a βavoiding permutation. ..."
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We investigate a new notion of approximately avoiding a permutation: π almost avoids β if one can remove a single entry from π to obtain a βavoiding permutation.
Universal cycles for permutation classes
"... Abstract. We define a universal cycle for a class of npermutations as a cyclic word in which each element of the class occurs exactly once as an nfactor. We give a general result for cyclically closed classes, and then survey the situation when the class is defined as the avoidance class of a set ..."
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Abstract. We define a universal cycle for a class of npermutations as a cyclic word in which each element of the class occurs exactly once as an nfactor. We give a general result for cyclically closed classes, and then survey the situation when the class is defined as the avoidance class of a set
Splittings and Ramsey properties of permutation classes
 arXiv:1307.0027 [math.CO]. Cited on
"... We say that a permutation pi is merged from permutations ρ and τ, if we can color the elements of pi red and blue so that the red elements are orderisomorphic to ρ and the blue ones to τ. A permutation class is a set of permutations closed under taking subpermutations. A permutation class C is spli ..."
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Cited by 1 (0 self)
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We say that a permutation pi is merged from permutations ρ and τ, if we can color the elements of pi red and blue so that the red elements are orderisomorphic to ρ and the blue ones to τ. A permutation class is a set of permutations closed under taking subpermutations. A permutation class C
Results 1  10
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188,220