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Expected Length of the Longest Common Subsequence of Multiple Strings

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arxiv 2504.10425 v1 pith:5AV6MXNS submitted 2025-04-14 math.CO cs.DMmath.PR

Expected Length of the Longest Common Subsequence of Multiple Strings

classification math.CO cs.DMmath.PR
keywords gammaasymptoticallyboundscommonderiveexpectedfraclength
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We study the generalized Chv\'atal-Sankoff constant $\gamma_{k,d}$, which represents the normalized expected length of the longest common subsequence (LCS) of $d$ independent uniformly random strings over an alphabet of size $k$. We derive asymptotically tight bounds for $\gamma_{2,d}$, establishing that $\gamma_{2,d} = \frac{1}{2} + \Theta\left(\frac{1}{\sqrt{d}}\right)$. We also derive asymptotically near-optimal bounds on $\gamma_{k,d}$ for $d\ge \Omega(\log k)$.

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