A Toeplitz matrix is constant along diagonals. A Hankel matrix is an upside-down Toeplitz matrix (hence constant on antidiagonals). What is the greatest |determinant| for the elementwise (aka Hadamard) product of two NxN sign matrices, one Toeplitz and one Hankel? The answer N det example matrix 1 0.00 -- 2 2.00 +---+- 3 4.00 ++----+--- 4 16.00 ++--+---+----- 5 48.00 -+++-+++-++------- 6 160.00 +--+++-++---+--------- 7 576.00 +--+---+-++---+----------- 8 4096.00 ++-+++--+---+---+-+-+--------- (Toeplitz specified by stating leftmost column going up, then continuing along top row going right, i.e. "clockwise"; then Hankel specified by stating top row going right, then continuing along rightmost column going down, i.e. "clockwise.") happens to match the maximum |determinant| for ANY matrix with real entries in [-1,1] given in http://oeis.org/A003433 ...at least it matches up to N=8. When (if ever) does Toeplitz*Hankel fail to reach optimality over all matrices?