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We investigate the variance of the length of the longest common subsequencesof two independent random words of size $n$, where the letters of one word arei.i.d. uniformly drawn from $\{\alpha_1, \alpha_2, \cdots, \alpha_m\}$, whilethe letters of the other word are i.i.d. drawn from $\{\alpha_1, \alpha_2,\cdots, \alpha_m, \alpha_{m+1}\}$, with probability $p > 0$ to be$\alpha_{m+1}$, and $(1-p)/m > 0$ for all the other letters. The order of thevariance of this length is shown to be linear in $n$.

On the Variance of the Length of the Longest Common Subsequences in Random Words With an Omitted Letter