A290279 - OEIS

%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