[seqfan] Sets of vectors over {0, 1}
Jens Voß
jens at voss-ahrensburg.de
Thu Feb 13 21:54:46 CET 2014
There is a very interesting puzzle on math stackexchange at the moment:
In http://math.stackexchange.com/questions/667257, the author asks for
the maximal size of a set S of n-tuples over {0, 1} such that all
subsets of S have different sum vectors. (In fact, the original question
asks for the value for n = 10.)
On contributor has reported to have come up with sets of sizes 4, 5, 7,
9, 11, 13, 15, 17 for n = 3, 4, 5, 6, 7, 8, 9, 10; but it is not at all
clear whether these values are in fact maximal.
As far as I can tell, the sequence is not in the database, or have I
missed something? Can anyone confirm at least some of the sizes to be in
fact maximal? I would expect a brute-force proof by calculation to be
very hard, so maybe somebody can come up with an idea for a smarter
approach?
Regards,
Jens
More information about the SeqFan
mailing list