Representative Strings Gallery

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 A zoomed-out view of a table of "representative strings".  (More colorful naming suggestions are welcome!)  There is a one-to-one correspondence between each overlap pattern table and its representative string table; each string s lines up with its overlap pattern p.  Most overlap patterns describe multiple strings, so there are many possible representative string tables for each overlap pattern table.



Some closeups:





























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What is an overlap pattern?

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An overlap pattern is a binary string that describes how a given character string overlaps shifted copies of itself.  For example, consider the string "abc". Its overlap pattern is "100".  For short, op("abc") = "100".  Here's another couple of examples: As we see, op("aba") = 101.  And op("aabaa") = "10011".      For a string s of length n, with characters indexed from 0 to n-1, the kth digit of op(s) = 1 if and only if the first n-k characters of s match its last n-k characters (in order.)  Notice that since every string matches itself, every overlap pattern starts with "1". What is an overlap pattern table? There is an OP table for every positive integer.  (We can debate whether or how to define one for n = 0.)  It consists of every possible overlap pattern of length n, arranged in increasing numeric order.  For n = 1, every string s of length 1 has op(s) = "1", so OP table n = 1 consists o...
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