Six Little Squares and How Their Numbers Grow
Department of Mathematics
San Francisco State University
1600 Holloway Avenue
San Francisco, CA 94132
Department of Mathematical Sciences
Binghamton, NY 13902-6000
We count the 3 × 3 magic, semimagic, and magilatin
squares, as functions either of the magic sum or of an upper bound on
the entries in the square. Our results on magic and semimagic squares
differ from previous ones, in that we require the entries in the square
to be distinct from each other and we derive our results not by
ad hoc reasoning, but from the general geometric and algebraic
method of our paper "An enumerative geometry for magic and magilatin
labellings". Here we illustrate that method with a detailed analysis
of 3 × 3 squares.
Full version: pdf,
(Concerned with sequences
Received March 9 2010;
revised version received June 1 2010.
Published in Journal of Integer Sequences, June 2 2010.
Revised, June 8 2010.
Journal of Integer Sequences home page