Longest alternating subsequences of k-ary words

Toufik Mansour

doi:10.1016/j.dam.2007.09.009

Longest alternating subsequences of k-ary words

Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 sequence a, b, c, d, ... is alternating if a > b < c > d < ⋯. 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.

Original language	English
Pages (from-to)	119-124
Number of pages	6
Journal	Discrete Applied Mathematics
Volume	156
Issue number	1
DOIs	https://doi.org/10.1016/j.dam.2007.09.009
State	Published - 1 Jan 2008

Keywords

Alternating sequence
Generating function
k-Ary word

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2007.09.009

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AB - 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 sequence a, b, c, d, ... is alternating if a > b < c > d < ⋯. 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.

KW - Alternating sequence

KW - Generating function

KW - k-Ary word

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ER -

Longest alternating subsequences of k-ary words

Abstract

Keywords

ASJC Scopus subject areas

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