On the distribution of the permanent of cyclic (0,1) matrices

Some results are obtained on the permanent of cyclic (0,1) matrices which support the conjecture that for such matrices of prime order p the number of distinct values the permanent attains is of order p. Writing e(r) for the number of distinct values the permanent of cyclic (0,1) matrices of order n can attain we found e(5) = 6, e(6) = 12, e(7) = 9, e(8) = 11, e(9) = 21, e(10) ≤ 44, and e(11) ≤ 30. It is easy to show e(p) ≤ 1/p(2p-2)+2, p prime, but these answers are considerably smaller. We obtain formulae for the permanent of cyclic (0,1) matrices in several cases

Unix and Linux administration handbook. Fifth edition

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