Pattern Popularity in 132-Avoiding Permutations
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...
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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
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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 ...
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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...
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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(...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2013
ISSN: 1077-8926
DOI: 10.37236/2634