OFFSET
0,2
COMMENTS
Consider an alphabet with two letters, say {0,1}. For two words v and w over this alphabet, we say v embeds in w, or v is a subsequence of w, if v can be obtained from w by erasing some (occurrences of) letters.
For a natural number n, define two words to be n-equivalent if they have the same subsequences of length up to n. The n-th term of this sequence is the number of equivalence classes of this equivalence relation.
LINKS
Prateek Karandikar and Philippe Schnoebelen, On the index of Simon's congruence for piecewise testability, arXiv:1310.1278 [cs.FL], 2013-2014.
EXAMPLE
For n=1, here are representatives of each of the four equivalence classes (taking the alphabet to be {0,1}) : empty word, 0, 1, 01.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Prateek Karandikar and Philippe Schnoebelen, Oct 09 2013
STATUS
approved