[HM] Gale(s)

Antreas P. Hatzipolakis (xpolakis@otenet.gr)
Thu, 16 Sep 1999 22:46:35 +0300 (EET DST)

Richard Guy <rkg@cpsc.ucalgary.ca> wrote (in part; in math-fun list):

> It arises [= the problem] from generalizing problem 124 of a book
> which Loren Larson has translated from the Swedish of Paul Vaderlind,
> and which we are embellishing in the hope of its appearing in the
> MAA's Spectrum Series.
>
> Find an n x n matrix whose entries are all zero, plus or minus one,
> and whose row sums and column sums are all distinct.
>
> This isn't too hard to do if n is even, but if n is odd, I believe
> it to be impossible. Proof or counter-example ????

Later he wrote:

> Doron Zeilberger says it's reminiscent of Gales's [Gale's ?] theorem on
> row sums and column sums. Anyone know what that is, whether it's relevant,
> and where is there a proof?

Who was Gale or Gales? And which is his theorem on matrix row/column sums?

Antreas