Patterns in Random Permutations Avoiding the Pattern 132
نویسندگان
چکیده
منابع مشابه
Pattern Popularity in 132-Avoiding Permutations
The popularity of a pattern p is the total number of copies of p within all permutations of a set. We address popularity in the set of 132-avoidng permutations. Bóna showed that in this set, all other non-monotone length-3 patterns are equipopular, and proved equipopularity relations between some length-k patterns of a specific form. We prove equipopularity relations between general length-k pa...
متن کاملPatterns in Random Permutations Avoiding
We consider a random permutation drawn from the set of 132-avoiding permutations of length n and show that the number of occurrences of another pattern σ has a limit distribution, after scaling by n where λ(σ) is the length of σ plus the number of descents. The limit is not normal, and can be expressed as a functional of a Brownian excursion. Moments can be found by recursion.
متن کاملRestricted 132-avoiding permutations
We study generating functions for the number of permutations on n letters avoiding 132 and an arbitrary permutation τ on k letters, or containing τ exactly once. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05
متن کاملThe equidistribution of some vincular patterns on 132-avoiding permutations
A pattern in a permutation π is a sub-permutation of π, and this paper deals mainly with length three patterns. In 2012 Bóna showed the rather surprising fact that the cumulative number of occurrences of the patterns 231 and 213 are the same on the set of permutations avoiding 132, even though the pattern based statistics 231 and 213 do not have the same distribution on this set. Here we show t...
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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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2016
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548316000171