A049475 Number of 2n X 2n matrices whose entries are {0,-1,+1} and whose row sums and column sums are all distinct.

1, 4, 39, 2260, 1338614, 8522456190

Offset: 1

Author

Michael Kleber

Keywords

• nonn
• nice
• hard

Comments

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

Examples

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

References

• It is known (see references) that a (2n+1) X (2n+1) matrix of this form cannot exist.
• 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.
• Fred Galvin, posting to sci.math, Date: 1999-09-25 - Solution to the antimagic 0,1,-1 matrix problem.

Links

• Denis Cazor, Notes for a talk
• Denis Cazor, Programme Pascal
• Eric Weisstein's World of Mathematics, Integer Matrix

Crossrefs

Cf. A049526, A049527.

Extensions

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

a(6) from Denis Cazor, Dec 06 2017