Permutation Patterns and Continued Fractions
نویسندگان
چکیده
منابع مشابه
Permutation Patterns and Continued Fractions
We find, in the form of a continued fraction, the generating function for the number of (132)-avoiding permutations that have a given number of (123) patterns, and show how to extend this to permutations that have exactly one (132) pattern. We also find some properties of the continued fraction, which is similar to, though more general than, those that were studied by Ramanujan. the electronic ...
متن کاملMarch 7, 2002 PERMUTATION PATTERNS, ORDERED TREES AND CONTINUED FRACTIONS
We enumerate permutations which have exactly r 123-patterns and s 132patterns where r + s ≤ 2. We also give a new bijection between the ordered trees on n+1 vertices and 123-avoiding permutations of length n. We define the weight of ordered trees so that the bijection becomes weight-preserving, and find the generating function, in the form of a continued fraction, of 123-avoiding permutations o...
متن کاملContinued Fractions and Generalized Patterns
Babson and Steingrimsson (2000, Séminaire Lotharingien de Combinatoire, B44b, 18) introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Let fτ ;r (n) be the number of 1-3-2-avoiding permutations on n letters that contain exactly r occurrences of τ , where τ is a generalized pattern on k letters. Let Fτ ...
متن کاملContinued Fractions, Statistics, And Generalized Patterns
Recently, Babson and Steingrimsson (see [BS]) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Following [BCS], let ekπ (respectively; fkπ) be the number of the occurrences of the generalized pattern 12-3. . . -k (respectively; 21-3. . . -k) in π. In the present note, we study the distribution of ...
متن کاملPeriodic Continued Fractions And
We investigate when an algebraic function of the form φ(λ) = −B(λ)+ √ R(λ) A(λ) , where R(λ) is a polynomial of odd degree N = 2g + 1 with coefficients in C, can be written as a periodic α-fraction of the form
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1999
ISSN: 1077-8926
DOI: 10.37236/1470