|
%I #12 Mar 31 2018 16:58:53
%S 1,1,2,6,22,110,628,4396,34496,309230,3069808
%N Number of permutations of [n] with a unique pair of orthogonal (diagonal, antidiagonal) X-rays.
%C The X-rays of a permutation are sequences of (diagonal, antidiagonal) sums of the corresponding permutation matrix.
%C A unique pair of orthogonal (diagonal, antidiagonal) X-rays allows identification of the permutation.
%H C. Bebeacua, T. Mansour, A. Postnikov and S. Severini, <a href="https://arxiv.org/abs/math/0506334">On the X-rays of permutations</a>, arXiv:math/0506334 [math.CO], 2005.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_matrix">Permutation matrix</a>
%e a(4) = 22. All permutations of {1,2,3,4} have unique pairs of orthogonal X-rays except 2413 and 3142, which share the same pair (0110110, 0110110):
%e .
%e . 0110110 . 0110110
%e . \\\+--\-+ . \\\+--\-+
%e . 2 \\| 1 | . 3 \\| 1 |
%e . 4 \| 1| . 1 \|1 |
%e . 1 /|1 | . 4 /| 1|
%e . 3 //| 1 | . 2 //| 1 |
%e . ///+--/-+ . ///+--/-+
%e . 0110110 . 0110110
%Y Cf. A289971, A290280.
%K nonn,more
%O 0,3
%A _Alois P. Heinz_, Jul 25 2017
| 