A332637 - OEIS

%I #24 Feb 22 2020 05:45:34

%S 1,2,8,68,1270,53200,5068960,1109820882,562711290616,664773220895406

%N The number of n X n replace matrices: binary matrices A where the i-th row contains exactly i zeros and A[i,j] >= A[j,i] for all i < j.

%C Defined in Felsner, Definition 2.

%H Stefan Felsner, <a href="http://page.math.tu-berlin.de/~felsner/Paper/numarr.pdf">On the number of arrangements of pseudolines</a>, preprint.

%H Stefan Felsner, <a href="https://doi.org/10.1007/PL00009318">On the number of arrangements of pseudolines</a>, Discrete & Computational Geometry, 18 (1997), 257-267.

%F According to [Felsner, Theorem 2] the number is at most 2^(0.6974*n^2) for large n.

%e For n = 3, all nine 0-1-matrices with the correct number of zeros and ones in each row are replace matrices except

%e     [ 1 0 1 ]

%e A = [ 1 0 0 ]

%e     [ 0 0 0 ]

%K nonn,more

%O 1,2

%A _Günter Rote_, Feb 18 2020

%E a(8)-a(9) from _Giovanni Resta_, Feb 19 2020

%E a(10) from _Giovanni Resta_, Feb 21 2020