Longest alternating subsequences of k-ary words

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)119-124
Number of pages6
JournalDiscrete Applied Mathematics
Issue number1
StatePublished - 1 Jan 2008


  • Alternating sequence
  • Generating function
  • k-Ary word

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'Longest alternating subsequences of k-ary words'. Together they form a unique fingerprint.

Cite this