Longest alternating subsequences of k-ary words
نویسنده
چکیده
Recently, Stanley [Longest alternating subsequences of permutations, preprint, arXiv/0511419v1] studied the length of the longest alternating subsequence of a permutation in the symmetric group,where a sequencea, b, c, d, . . . isalternating ifa >bd < · · ·. In this paper, we extend this result to the case of k-ary words. More precisely, we find an explicit formula for the generating function of the number of k-ary words of length n according to the length of the longest alternating subsequence. © 2007 Elsevier B.V. All rights reserved. MSC: 05A05; 05A15; 05A16
منابع مشابه
Longest alternating subsequences in pattern-restricted k-ary words
We study the generating functions for pattern-restricted k-ary words of length n corresponding to the longest alternating subsequence statistic in which the pattern is any one of the six permutations of length three.
متن کاملLongest Alternating Subsequences in Pattern-Restricted Permutations
Inspired by the results of Stanley and Widom concerning the limiting distribution of the lengths of longest alternating subsequences in random permutations, and results of Deutsch, Hildebrand and Wilf on the limiting distribution of the longest increasing subsequence for pattern-restricted permutations, we find the limiting distribution of the longest alternating subsequence for pattern-restric...
متن کاملLongest Alternating Subsequences of Permutations
The length is(w) of the longest increasing subsequence of a permutation w in the symmetric group Sn has been the object of much investigation. We develop comparable results for the length as(w) of the longest alternating subsequence of w, where a sequence a, b, c, d, . . . is alternating if a > b < c > d < · · · . For instance, the expected value (mean) of as(w) for w ∈ Sn is exactly (4n + 1)/6...
متن کاملOn the Limiting Distribution for the Longest Alternating Sequence in a Random Permutation
Recently Richard Stanley [3] initiated a study of the distribution of the length asn(w) of the longest alternating subsequence in a random permutation w from the symmetric group Sn. Among other things he found an explicit formula for the generating function (on n and k) for Pr (asn(w) ≤ k) and conjectured that the distribution, suitably centered and normalized, tended to a Gaussian with varianc...
متن کاملLongest Monotone Subsequences and Rare Regions of Pattern-Avoiding Permutations
We consider the distributions of the lengths of the longest monotone and alternating subsequences in classes of permutations of size n that avoid a specific pattern or set of patterns, with respect to the uniform distribution on each such class. We obtain exact results for any class that avoids two patterns of length 3, as well as results for some classes that avoid one pattern of length 4 or m...
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:
- Discrete Applied Mathematics
دوره 156 شماره
صفحات -
تاریخ انتشار 2008