TABLEAU 1 --------- ORIGINAL MATRIX M1: +-123456789 123456789 123456789 123456789 12 1 111111111100000000000000010010010010000000 2 100100000000000000000000000000000000000000 3 000000000000000000000000000000000000000000 4 000000000000000000000000000000000000000000 5 101111001100000000000000000000010000000000 6 000001000000000000000000000000000000000000 7 000000000000000000000000000000000000000000 8 100100011000000000000000010000010010000000 9 000100000100000000000000000000000000000000 000100000100000000000000000000000000000000 1 000000000001100000000000000000000000000000 2 000000000000111000000000000000000000000100 3 100000000011111100110100000000000000010110 4 111111001101111100111100111110111111110110 5 000000000000001000000000000000000000000000 6 000000000000000110000000000000000000000000 7 000000000000111011000000010000000000000100 8 000000100100011000000000100000000000000100 9 101011000001111010101000110010000010000110 000000000000101010111001010000000000001010 1 111111011100111111111011111110110000011110 2 011111111111111111101111111111111111011010 3 000110000001111011101011010010010000001000 4 000100000100111010111001110000100000001000 5 011101111111111111111111111111111111111000 6 100000010011001100101100010010110010010100 7 100000000010011100001100111100000001001110 8 000000100000010000000000000100000001000000 9 000000000000000000000000000011100000000100 011111111111111111111111111111111111111110 1 011111111111111111111111111111111111111110 2 100000000000001000000000000100011101111000 3 000000000000000000000000000000001000000000 4 100000000000000000000000000100011000000000 5 000000000000001000000000010100111011100000 6 000000000000000000000000000000000001000000 7 100000000000000000000000000000000000000000 8 000000000000011000000000000000000000010000 9 100000000000010000000000000100011000000100 011111011111111111101100111010110010010010 1 110011010011110110101110011000000000000010 2 000000000000000000000000000000000000000000 TABLEAU 1 --------- EVENTUAL CONNECTION MATRIX C1: +-123456789 123456789 123456789 123456789 12 1 111111111111111111111111111111111111111110 2 111111111111111111111111111111111111111110 3 000000000000000000000000000000000000000000 4 000000000000000000000000000000000000000000 5 111111111111111111111111111111111111111110 6 000001000000000000000000000000000000000000 7 000000000000000000000000000000000000000000 8 111111111111111111111111111111111111111110 9 000100000100000000000000000000000000000000 000100000100000000000000000000000000000000 1 111111111111111111111111111111111111111110 2 111111111111111111111111111111111111111110 3 111111111111111111111111111111111111111110 4 111111111111111111111111111111111111111110 5 000000000000001000000000000000000000000000 6 111111111111111111111111111111111111111110 7 111111111111111111111111111111111111111110 8 111111111111111111111111111111111111111110 9 111111111111111111111111111111111111111110 111111111111111111111111111111111111111110 1 111111111111111111111111111111111111111110 2 111111111111111111111111111111111111111110 3 111111111111111111111111111111111111111110 4 111111111111111111111111111111111111111110 5 111111111111111111111111111111111111111110 6 111111111111111111111111111111111111111110 7 111111111111111111111111111111111111111110 8 111111111111111111111111111111111111111110 9 111111111111111111111111111111111111111110 111111111111111111111111111111111111111110 1 111111111111111111111111111111111111111110 2 111111111111111111111111111111111111111110 3 000000000000000000000000000000001000000000 4 111111111111111111111111111111111111111110 5 111111111111111111111111111111111111111110 6 000000000000000000000000000000000001000000 7 111111111111111111111111111111111111111110 8 111111111111111111111111111111111111111110 9 111111111111111111111111111111111111111110 111111111111111111111111111111111111111110 1 111111111111111111111111111111111111111110 2 000000000000000000000000000000000000000000 TABLEAU 1 --------- Eigenvalues of C1: {0,...,0,1,1,1,1,1,32} Bases for eigenspaces of nonzero eigenvalues: null(C1-32*I) null(C1-1*I) ------------- ------------------------- 1 1 1 0 0 0 0 1 2 1 2 0 0 0 0 1 3 0 3 0 0 0 0 0 4 0 4 0 0 0 0 0 5 1 5 0 0 0 0 1 6 0 6 -2 -1 -1 -1 -31 7 0 7 0 0 0 0 0 8 1 8 0 0 0 0 1 9 0 9 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 2 1 2 0 0 0 0 1 3 1 3 0 0 0 0 1 4 1 4 0 0 0 0 1 5 0 5 0 1 0 0 0 6 1 6 0 0 0 0 1 7 1 7 0 0 0 0 1 8 1 8 0 0 0 0 1 9 1 9 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 2 1 2 0 0 0 0 1 3 1 3 0 0 0 0 1 4 1 4 0 0 0 0 1 5 1 5 0 0 0 0 1 6 1 6 0 0 0 0 1 7 1 7 0 0 0 0 1 8 1 8 0 0 0 0 1 9 1 9 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 2 1 2 0 0 0 0 1 3 0 3 0 0 1 0 0 4 1 4 0 0 0 0 1 5 1 5 0 0 0 0 1 6 0 6 0 0 0 1 0 7 1 7 0 0 0 0 1 8 1 8 0 0 0 0 1 9 1 9 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 2 0 2 0 0 0 0 0 Maximal cycle for tableau 1 (32 vertices): {1,2,5,8,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30, 31,32,34,35,37,38,39,40,41}