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A290280
Number of pairs of orthogonal (diagonal, antidiagonal) X-rays for all permutations of [n].
2
1, 1, 2, 6, 23, 115, 674, 4718, 37371, 335435, 3340116
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
C. Bebeacua, T. Mansour, A. Postnikov and S. Severini, On the X-rays of permutations, arXiv:math/0506334 [math.CO], 2005.
Wikipedia, Permutation
EXAMPLE
a(4) = 23. 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
Sequence in context: A117158 A317128 A185334 * A349087 A370508 A370670
KEYWORD
nonn,more
AUTHOR
Alois P. Heinz, Jul 25 2017
STATUS
approved