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A229954 The index of Simon's piecewise testability congruence, for words of length 2 over an n-letter alphabet. 0

%I #27 Apr 18 2022 10:14:30

%S 3,16,152,2326,52132,1602420,64529264

%N The index of Simon's piecewise testability congruence, for words of length 2 over an n-letter alphabet.

%C Consider an alphabet with n letters, say {a_0, a_1, ... a_{n-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.

%C Define two words to be 2-equivalent if they have the same subsequences of length up to 2. The n-th term of this sequence is the number of equivalence classes of this equivalence relation, when the size of the alphabet is n.

%H Prateek Karandikar and Philippe Schnoebelen, <a href="http://arxiv.org/abs/1310.1278">On the index of Simon's congruence for piecewise testability</a> arXiv:1310.1278 [cs.FL], 2013-2014.

%e For n=1, with the alphabet {a_0}, representatives of the three equivalence classes are: empty word, a_0, a_0a_0.

%K nonn,more

%O 1,1

%A _Prateek Karandikar_ and _Philippe Schnoebelen_, Oct 09 2013

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Last modified July 19 00:30 EDT 2024. Contains 374388 sequences. (Running on oeis4.)