**Author:**
Federico Bonetto Heinrich Matzinger

**Title:** *
Fluctuations Of The Longest Common
Subsequence In The Asymmetric Case Of 2- And 3-Letter Alphabets*

**Abstract: **
We investigate the asymptotic standard deviation of the
Longest Common Subsequence (LCS) of two independent i.i.d. sequences
of length $n$. The first sequence is drawn from a three letter
alphabet {0,1,a}, whilst the second sequence is binary. The main
result of this article is that in this asymmetric case, the standard
deviation of the length of the LCS is of order square root of
n. This confirms Waterman's conjecture Waterman-estimation for this
special case. Our result seems to indicate that in many other
situations the order of the standard deviation is also square root
of n.

**Keywords:**
Sequence comparison, longest common subsequnce

Federico Bonetto

School of Mathematics

Gerogia Institute of Technology

Atlanta, GA 30309

email: bonetto@math.gatech.edu

Heinrich Matzinger

School of Mathematics

Gerogia Institute of Technology

Atlanta, GA 30309

email: matzi@math.gatech.edu