منابع مشابه
Shape Avoiding Permutations
Permutations avoiding all patterns of a given shape (in the sense of Robinson-Schensted-Knuth) are considered. We show that the shapes of all such permutations are contained in a suitable thick hook, and deduce an exponential growth rate for their number.
متن کاملThe Shape of Random Pattern-avoiding Permutations
We initiate the study of limit shapes for random permutations avoiding a given pattern. Specifically, for patterns of length 3, we obtain delicate results on the asymptotics of distributions of positions of numbers in the permutations. We view the permutations as 0-1 matrices to describe the resulting asymptotics geometrically. We then apply our results to obtain a number of results on distribu...
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We study the problem of counting alternating permutations avoiding collections of permutation patterns including 132. We construct a bijection between the set Sn(132) of 132-avoiding permutations and the set A2n+1(132) of alternating, 132avoiding permutations. For every set p1, . . . , pk of patterns and certain related patterns q1, . . . , qk, our bijection restricts to a bijection between Sn(...
متن کاملPattern Avoiding Permutations
We establish a bijection from the set of all permutations (of a given length) that avoid a pattern q and a context-sensitive language.
متن کاملPermutations Avoiding Arithmetic Patterns
A permutation π of an abelian group G (that is, a bijection from G to itself) will be said to avoid arithmetic progressions if there does not exist any triple (a, b, c) of elements of G, not all equal, such that c − b = b − a and π(c) − π(b) = π(b) − π(a). The basic question is, which abelian groups possess such a permutation? This and problems of a similar nature will be considered. 1 Notation...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2002
ISSN: 0097-3165
DOI: 10.1006/jcta.2001.3202