منابع مشابه
Restricted Permutations by 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. In this paper we study the generating functions for the number of permutations on n letters avoiding a generalized pattern ab-c where (a, b, c) ∈ S3, and containing a prescribed number of occurrences of ...
متن کاملRestricted growth function patterns and statistics∗
A restricted growth function (RGF) of length n is a sequence w = w1w2 . . . wn of positive integers such that w1 = 1 and wi ≤ 1 + max{w1, . . . , wi−1} for i ≥ 2. RGFs are of interest because they are in natural bijection with set partitions of {1, 2, . . . , n}. RGF w avoids RGF v if there is no subword of w which standardizes to v. We study the generating functions ∑ w∈Rn(v) q st(w) where Rn(...
متن کاملRestricted Single or Double Signed Patterns
Let E n = {[τ ]a = (τ (a1) 1 , . . . , τ (an) n )|τ ∈ Sn, 1 ≤ ai ≤ r} be the set of all signed permutations on the symbols 1, 2, . . . , n with signs 1, 2, . . . , r. We prove, for every 2-letter signed pattern [τ ]a, that the number of [τ ]a-avoiding signed permutations in E n is given by the formula n ∑ j=0 j!(r−1) ( n j 2 . Also we prove that there are only one Wilf class for r = 1, four Wil...
متن کاملPermutations with Restricted Patterns and Dyck Paths
We exhibit a bijection between 132-avoiding permutations and Dyck paths. Using this bijection, it is shown that all the recently discovered results on generating functions for 132-avoiding permutations with a given number of occurrences of the pattern 12 . . . k follow directly from old results on the enumeration of Motzkin paths, among which is a continued fraction result due to Flajolet. As a...
متن کاملWhat Does the Future Hold for Restricted Patterns?
As one can see, without several examples worked out with a pencil and paper, this formal definition is not very insightful. To understand where restricted patterns really originated from, we draw on visual imagery and replace “one-dimensional” permutations by “twodimensional” objects, matrices. In doing so, we shall violate the customary labeling of the top row as the “first” row of a matrix. I...
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: Journal of Combinatorial Theory, Series A
سال: 1972
ISSN: 0097-3165
DOI: 10.1016/0097-3165(72)90100-8