The Shape of Random Pattern-avoiding Permutations
نویسندگان
چکیده
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 distributions of permutation statistics.
منابع مشابه
Generating Trees and Pattern Avoidance in Alternating Permutations
We extend earlier work of the same author to enumerate alternating permutations avoiding the permutation pattern 2143. We use a generating tree approach to construct a recursive bijection between the set A2n(2143) of alternating permutations of length 2n avoiding 2143 and the set of standard Young tableaux of shape 〈n, n, n〉, and between the set A2n+1(2143) of alternating permutations of length...
متن کاملBeyond Alternating Permutations: Pattern Avoidance in Young Diagrams and Tableaux
We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particular, we extend Babson-West’s notion of shape-Wilf equivalence to apply to alternating permutations and so generalize results of Backelin-West-Xin and Ouchterlony to alternating permutations. Second, we study pattern a...
متن کاملPattern avoidance and RSK-like algorithms for alternating permutations and Young tableaux
We define a class Ln,k of permutations that generalizes alternating (up-down) permutations. We then give bijective proofs of certain pattern-avoidance results for this class. The bijections employed include are a modified form of the RSK insertion algorithm and a different bijection with RSK-like properties. As a special case of our results, we give two bijections between the set A2n(1234) of a...
متن کاملWhole mirror duplication-random loss model and pattern avoiding permutations
a r t i c l e i n f o a b s t r a c t Keywords: Algorithms Combinatorial problems Pattern avoiding permutation Whole duplication-random loss model Genome Generating algorithm Binary reflected Gray code In this paper we study the problem of the whole mirror duplication-random loss model in terms of pattern avoiding permutations. We prove that the class of permutations obtained with this model af...
متن کامل2 00 3 Longest increasing subsequences in pattern - restricted permutations
Inspired by the results of Baik, Deift and Johansson on the limiting distribution of the lengths of the longest increasing subsequences in random permutations, we find those limiting distributions for pattern-restricted permutations in which the pattern is any one of the six patterns of length 3. We show that the (132)-avoiding case is identical to the distribution of heights of ordered trees, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013