A290279 Number of permutations of [n] with a unique pair of orthogonal (diagonal, antidiagonal) X-rays.

1, 1, 2, 6, 22, 110, 628, 4396, 34496, 309230, 3069808

Offset

0,3

Comments

The X-rays of a permutation are sequences of (diagonal, antidiagonal) sums of the corresponding permutation matrix.

A unique pair of orthogonal (diagonal, antidiagonal) X-rays allows identification of the permutation.

Links

Table of n, a(n) for n=0..10.

C. Bebeacua, T. Mansour, A. Postnikov and S. Severini, On the X-rays of permutations, arXiv:math/0506334 [math.CO], 2005.

Wikipedia, Permutation

Wikipedia, Permutation matrix

Example

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):
.
.  0110110       .  0110110
.   \\\+--\-+    .   \\\+--\-+
.  2 \\| 1  |    .  3 \\|  1 |
.  4  \|   1|    .  1  \|1   |
.  1  /|1   |    .  4  /|   1|
.  3 //|  1 |    .  2 //| 1  |
.   ///+--/-+    .   ///+--/-+
.  0110110       .  0110110

Crossrefs

Cf. A289971, A290280.

Sequence in context: A375131 A216720 A174074 * A014371 A374618 A111280

Adjacent sequences: A290276 A290277 A290278 * A290280 A290281 A290282

Keyword

nonn,more

Author

Alois P. Heinz, Jul 25 2017

Status

approved