Starting at N = 29 using the values of -1 and + 1 given by Warren and using Maple with Digits = 1000, I get different values when I round his determinants to the nearest integer. For example, for N = 29 I get Maple's value = -668472148627227148288 Warren's value = 668472148627227148000 It seems that in Warren's numbers there are not enough significant digits above N = 28. Also in the case of N = 29 I get a different sign for the determinant. --Edwin On Fri, Aug 31, 2012 at 2:43 PM, Neil Sloane <njasloane@gmail.com> wrote:
Warren, how many of those terms can be relied on?
On Fri, Aug 31, 2012 at 1:52 PM, Warren Smith <warren.wds@gmail.com> wrote:
NxN circulant matrices with entries +-1 and maximum |determinant| (Matrices specified by stating top row.) N det example matrix 1 1 + 2 0 +- 3 4 -++ 4 -16 +--- 5 48 -++++ 6 -128 +----- 7 512 --+-+++ 8 2304 ++-+---- 9 6912 -+-++-+++ 10 22528 ++-+---+-- 11 273408 -+-+--+++++ 12 2097152 ++++--+-+++- 13 14929920 --+-+++++-+++ 14 -50331648 ++--+-+------- 15 390905856 +---++-+-+++++- 16 -1644167168 +---+-+++--+---- 17 12279939072 ++-+++--++-+---++ 18 69660573696 +++++-++--+-+-++-- 19 865782202368 +++--+++-+----++-++ 20 5566277615616 +-+--++-++++++--+++- 21 41248865910784 ---+-+++-++-++++-++++ 22 -215055782117376 +-+----+--+--++---+++- 23 2385859554836480 +-+---+-++-++++-+++--++ 24 25783171861708800 ++++-++-+-+---+--+++++-- 25 146322302697472000 +-+----++-++++--+++-++-++ 26 1107244165160239104 ++-++---+-++-+-+-----+---- 27 11063259546716733440 -+--+-+---+++++-++--+++-+++ 28 -76787161889935196160 +---+++---+--+++-+--+-+-----
29 6.68472148627227148e+20 -+-+-++-++-----+++----+---+-- 30 5.81509024420837982e+21 -+-+-+-+--+--+-------++++--++- 31 7.30634230169889910e+22 --+-+++-+++---++++++-+-++-+--+- 32 6.07251019096056018e+23 -+-+++-++--------++----+++--+--+ 33 6.83936575994044069e+24 -+---+++-++----+-++-++---+-+----- 34 4.49603940530125316e+25 ---++-------+-+--++++---+-+--++--+ 35 5.73365205894426472e+26 -+++-+-+--+--++-----++-+----+---+++ 36 6.80750852248195719e+27 -++-++++-+-+-+----++--+++++--+--++++ 37 5.41106751627075914e+28 --++-+---+---+-++---+++-++-+-++------ 38 4.39152787578415089e+29 -++-++---+---+-+--++----+-----++++-+-+ 39 6.32198265057225110e+30 --+-+++-+++--++++-+-++-+----+---+-+++++ 40 6.43984299466058275e+31 -+++---+-++---++-+-+---------++-++--+-++
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