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In the study of permutations and permutation patterns, a permutation class is a set of permutations such that every pattern within a permutation in is also in . In other words, a permutation class is a hereditary property of permutations, or a downset in the permutation pattern order.A permutation class may also be known as a pattern class, closed class, or simply class of permutations. (a tight bound on the base of the exponential growth rate) exists for all principal permutation classes, it is open whether it exists for all other permutation classes.

Attributes	Values
rdfs:label	Permutation class (en)
rdfs:comment	In the study of permutations and permutation patterns, a permutation class is a set of permutations such that every pattern within a permutation in is also in . In other words, a permutation class is a hereditary property of permutations, or a downset in the permutation pattern order.A permutation class may also be known as a pattern class, closed class, or simply class of permutations. (a tight bound on the base of the exponential growth rate) exists for all principal permutation classes, it is open whether it exists for all other permutation classes. (en)
dcterms:subject	Permutation patterns
Wikipage page ID	40940518 (xsd:integer)
Wikipage revision ID	998281446 (xsd:integer)
Link from a Wikipage to another Wikipage	Enumerations of specific permutation classes Permutation Richard P. Stanley Upper bound Wilf equivalence Permutation patterns Combinatorial class Stack-sortable permutation Adam Marcus (mathematician) Equivalence relation Gábor Tardos Herbert Wilf Stanley–Wilf conjecture Hereditary property Ideal (order theory) Permutation pattern
sameAs	Permutation class Permutation class
dbp:wikiPageUsesTemplate	dbt:R dbt:Reflist
has abstract	In the study of permutations and permutation patterns, a permutation class is a set of permutations such that every pattern within a permutation in is also in . In other words, a permutation class is a hereditary property of permutations, or a downset in the permutation pattern order.A permutation class may also be known as a pattern class, closed class, or simply class of permutations. Every permutation class can be defined by the minimal permutations which do not lie inside it, its basis. A principal permutation class is a class whose basis consists of only a single permutation. Thus, for instance, the stack-sortable permutations form a principal permutation class, defined by the forbidden pattern 231. However, some other permutation classes have bases with more than one pattern or even with infinitely many patterns. A permutation class that does not include all permutations is called proper.In the late 1980s, Richard Stanley and Herbert Wilf conjectured that for every proper permutation class , there is some constant such that the number of length- permutations in the class is upper bounded by . This was known as the Stanley–Wilf conjecture until it was proved by Adam Marcus and Gábor Tardos.However although the limit (a tight bound on the base of the exponential growth rate) exists for all principal permutation classes, it is open whether it exists for all other permutation classes. Two permutation classes are called Wilf equivalent if, for every , both have the same number of permutations of length . Wilf equivalence is an equivalence relation and its equivalence classes are called Wilf classes. They are the combinatorial classes of permutation classes. The counting functions and Wilf equivalences among many specific permutation classes are known. (en)
prov:wasDerivedFrom	wikipedia-en:Permutation_class?oldid=998281446&ns=0
page length (characters) of wiki page	3498 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Permutation_class
is Link from a Wikipage to another Wikipage of	Enumerations of specific permutation classes List of conjectures Wilf equivalence Combinatorial class Stanley–Wilf conjecture Hereditary property
is foaf:primaryTopic of	wikipedia-en:Permutation_class

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