Sharp upper and lower bounds on the length of general Davenport-Schinzel sequences

Published

Journal Article

We obtain sharp upper and lower bounds on the maximal length λs(n) of (n, s)-Davenport-Schinzel sequences, i.e., sequences composed of n symbols, having no two adjacent equal elements and containing no alternating subsequence of length s + 2. We show that (i) λ4(n) = Θ(n·2α(n)); (ii) for s > 4, λs(n) ≤ n·2(α(n)) (s - 2) 2 + Cs(n) if s is even and λs(n) ≤ n·2(α(n)) (s - 3) 2log(α(n)) + Cs(n) if s is odd, where Cs(n) is a function of α(n) and s, asymptotically smaller than the main term; and finally (iii) for even values of s > 4, λs(n) = Ω(n·2Ks(α(n)) (s - 2) 2 + Qs(n)), where Ks = (( (s - 2) 2)!)-1 and Qs is a polynomial in α(n) of degree at most (s - 4) 2. © 1989.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Sharir, M; Shor, P

Published Date

  • January 1, 1989

Published In

Volume / Issue

  • 52 / 2

Start / End Page

  • 228 - 274

Electronic International Standard Serial Number (EISSN)

  • 1096-0899

International Standard Serial Number (ISSN)

  • 0097-3165

Digital Object Identifier (DOI)

  • 10.1016/0097-3165(89)90032-0

Citation Source

  • Scopus