falsely-identical sequences [repost]
Leroy Quet
qq-quet at mindspring.com
Fri Feb 6 00:48:08 CET 2004
(I am reposting this because I kept an old thread's title before by
accident. Sorry.)
David Wasserman's reply in "Max GCD Permutation Product":
>The two sequences first disagree at m = 14.
got me wondering (actually I wondered about this earlier) about sequences
in the EIS which match every term stored in the database, but are unequal
ultimately at higher-indexed terms.
We can have 3 situations with these false matches:
1) the 2 sequences are known to be different, and a comment about this
fact is mentioned on the sequences' EIS web-page.
2) the sequences are either just assumed wrongly to be identitical by the
contributers to the sequences' (common) web-page, or none of the
contributers have bothered to include in the database that the sequences
differ ultimately.
3) it is not known with certainty what the situation is regarding the
sequences being the same or differing. (and this uncertainty is mentioned
in the EIS )
(And, of course, perhaps a contributer assumed, using faulty mathematics,
that the sequences differed, which happens to be correct anyway.)
Or a single sequence can be falsely assumed to be 2 or more different
sequences as well.
Are these situations above common in the EIS? I cannot recall any
specific example of either.
But each of the above situations must occur at a significant rate, given
how many sequences are now in the database.
For fun, I ask here for interesting examples of the above situations.
And more seriously, I post this email as a warning for all of us when
making assumptions regarding sequences' sameness.
Actually, as far as the (now only finite-sized) EIS is concerned, are 2
sequences that have the same terms as far as the EIS database is
concerned, but differ at higher index(es), considered officially to be
the "same" sequence or different sequences?
thanks,
Leroy Quet
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