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
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
Extensions
Bodendiek-Burosch reference from torsten.sillke(AT)lhsystems.com
a(6) from Denis Cazor, Dec 06 2017
Comments