On the Longest $k$-Alternating Subsequence
نویسندگان
چکیده
We show that the longest k-alternating substring of a random permutation has length asymptotic to 2(n− k)/3.
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 of k-ary words
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 functio...
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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...
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 22 شماره
صفحات -
تاریخ انتشار 2015