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Inequalities for the Score Constant in Matching Random Sequences
Yunshyong Chow and Yu Zhang
Journal of Applied Probability
Vol. 36, No. 2 (Jun., 1999), pp. 601-606
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3215478
Page Count: 6
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We consider a sequence matching problem involving the optimal alignment score for contiguous sequences; rewarding matches and penalizing for deletions and mismatches. Arratia and Waterman conjectured in  that the score constant a(µ,δ) is a strictly monotone function (i) in δ for all positive δ and (ii) in µ if 0≤µ≤2δ. Here we prove that (i) is true for all δ and (ii) is true for some µ.
Journal of Applied Probability © 1999 Applied Probability Trust