Chvátal–Sankoff constants

In mathematics, the Chvátal–Sankoff constants are mathematical constants that describe the lengths of longest common subsequences of random strings. Although the existence of these constants has been proven, their exact values are unknown. They are named after Václav Chvátal and David Sankoff, who began investigating them in the mid-1970s.

There is one Chvátal–Sankoff constant ${\displaystyle \gamma _{k}}$ for each positive integer k, where k is the number of characters in the alphabet from which the random strings are drawn. The sequence of these numbers grows inversely proportionally to the square root of k. However, some authors write "the Chvátal–Sankoff constant" to refer to ${\displaystyle \gamma _{2}}$, the constant defined in this way for the binary alphabet.