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Number of 2n X 2n matrices whose entries are {0,-1,+1} and whose row sums and column sums are all distinct.
5

%I #36 Mar 29 2020 13:26:38

%S 1,4,39,2260,1338614,8522456190

%N Number of 2n X 2n matrices whose entries are {0,-1,+1} and whose row sums and column sums are all distinct.

%C Matrices differing by taking transpose, multiplying by -1 and permuting rows and columns are regarded as equivalent.

%D It is known (see references) that a (2n+1) X (2n+1) matrix of this form cannot exist.

%D Rainer Bodendiek, Gustav Burosch; Streifzüge durch die Kombinatorik, Aufgaben und Lösungen aus dem Schatz der Mathematik-Olympiaden, (Excursions into Combinatorics) Spektrum Akademischer Verlag, Heidelberg, 1995, ISBN 3-86025-393-X Kapitel: Aufgaben zu Invarianten, Aufgabe 5.30, pp. 250-253.

%D Fred Galvin, posting to sci.math, Date: 1999-09-25 - Solution to the antimagic 0,1,-1 matrix problem.

%H Denis Cazor, <a href="/A049475/a049475_4.pdf">Notes for a talk</a>

%H Denis Cazor, <a href="/A049475/a049475_5.pdf">Programme Pascal</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerMatrix.html">Integer Matrix</a>

%e A 2 X 2 example: [ 1 1; 0 -1 ].

%Y Cf. A049526, A049527.

%K nonn,nice,hard

%O 1,2

%A _Michael Kleber_

%E Bodendiek-Burosch reference from torsten.sillke(AT)lhsystems.com

%E a(6) from _Denis Cazor_, Dec 06 2017