On a speculated relation between chvátal–sankoff constants of several sequences

Authors:
M. Kiwi;J. Soto
Affiliations:
Departamento de ingeniería matemática, centro de modelamiento matemático (umi 2807, cnrs), university of chile (e-mail: mkiwi@dim.uchile.cl);Department of mathematics, mit, cambridge, ma 02139, usa (e-mail: jsoto@math.mit.edu)
Venue:
Combinatorics, Probability and Computing
Year:
2009

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Abstract

It is well known that, when normalized by n, the expected length of a longest common subsequence of d sequences of length n over an alphabet of size σ converges to a constant γσ,d. We disprove a speculation by Steele regarding a possible relation between γ2,d and γ2,2. In order to do that we also obtain some new lower bounds for γσ,d, when both σ and d are small integers.