login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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) = 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

Cf. A289971, A290279.

Sequence in context: A117158 A317128 A185334 * A059513 A132647 A177253

Adjacent sequences:  A290277 A290278 A290279 * A290281 A290282 A290283

KEYWORD

nonn,more

AUTHOR

Alois P. Heinz, Jul 25 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 19 03:54 EDT 2018. Contains 313843 sequences. (Running on oeis4.)