[seqfan] seq needed of (0,+-1) matrices

N. J. A. Sloane njas at research.att.com
Wed Jan 18 19:16:48 CET 2012

Dear Seq Fans, This paper:

MR2002770 (2004g:05108)
Wesp, Gerhard(A-SALZ-IM)
A note on the spectra of certain skew-symmetric {1,0,1}-matrices. (English summary)
Discrete Math. 258 (2002), no. 1-3, 339-346.

discusses matrices A = (a_ij) of size nxn with entries from {-1,0,+1}
which are skew-symmetric and have the additional property that

a_wx a_yz + a_wy a_zx + a_wz a_xy = a_wx a_wy a_wz a_xy a_xz a_yz ... (*)

for all distinct w,x,y,z in {1..n}.

But he does not count them. Can someone compute the first few terms?
Obviously a(1)=1 (the zero matrix),
a(2) = 3, a(3) = 27 (up to this point we get all skew-symmetric matrices)
and a(4) < 3^6 

(There seem to be several combinatorial applications)


More information about the SeqFan mailing list