โ Scribed by D.R. Stinson
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Readers wishing to make comments dealing with technical matters about a problem that has appeared should write to the correspondent for that particular problem. Comments of a general nature about previous problems should be sent to Professor Alspach.
Theorem (See [3] for a proof and definitions). Let S c lPd be Q set of at least (d + l)(r -1) + (k + I) strongly independent points, where 0 6 k G d. Then S has a partition S=SU-US' so that the k-dimensional volume V(k) = ~01&&l conv Si] satisfies V(k) > 0. If (r, k) = (2,0) this is Radon's theorem;
Given integers I-Z and 1p1, how many distinct solutions {a, b, c} are there to the system of equations a+b+c=m a\*+b\*+c\*=n with aabacaO? With the condition on the non-nq$iv, ,jr of aLs b and c removed, the problem was solved in [I]. A solution to the more constrained problem would have application