magicrect: Construct Magic Rectangles and Nearly Magic Rectangles
Constructs a magic rectangle or a nearly magic rectangle of
order p x q for every order for which one exists, together with
existence classification and verification utilities. A magic rectangle
arranges the integers 1 to p*q so that all row sums are equal and all
column sums are equal; it exists exactly when p and q have the same
parity, excluding 2 x 2 and degenerate single-row/column cases
(Hagedorn, 1999, <doi:10.1016/S0012-365X(99)00041-2>). When p and q have
opposite parity a nearly magic rectangle exists instead, with constant
sums along one direction and sums differing by at most one along the
other (Chai, Singh and Stufken, 2019, Journal of Combinatorial Designs
27(6), 368-376).
Implements the constructions of De Los Reyes, Das, Midha and Vellaisamy
(2009) for even by even orders, Chai, Das and Midha (2013) for odd by
odd orders, and Chai, Singh and Stufken (2019) for the nearly magic
(even by odd) case.
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