On the diagram of 132-avoiding permutations
نویسندگان
چکیده
منابع مشابه
On the diagram of 132-avoiding permutations
The diagram of a 132-avoiding permutation can easily be characterized: it is simply the diagram of a partition. Based on this fact, we present a new bijection between 132-avoiding and 321-avoiding permutations. We will show that this bijection translates the correspondences between these permutations and Dyck paths given by Krattenthaler and by Billey-Jockusch-Stanley, respectively, to each oth...
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 کاملEquipopularity Classes of 132-Avoiding Permutations
The popularity of a pattern p in a set of permutations is the sum of the number of copies of p in each permutation of the set. We study pattern popularity in the set of 132-avoiding permutations. Two patterns are equipopular if, for all n, they have the same popularity in the set of length-n 132-avoiding permutations. There is a well-known bijection between 132-avoiding permutations and binary ...
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 کاملPattern 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...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2003
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(03)00065-9