[seqfan] Number of high-dimensional permutations

Neil Sloane njasloane at gmail.com
Wed Oct 22 19:17:18 CEST 2014

The latest issue of Combinatorica (vol 34 #4) has an article by Linial/Luria
about the number of "d-dimensional permutations",  see also arXiv:1106.0649.
Definition: an nXnXn...n = n^(d+1) array of 0's and 1's with
exactly one 1 in each row, column, ,...line, .
An ordinary permutation is the case d =1 (ordinary matrices
with a single 1 in each row and column)

So what is the array of these numbers?
Row 1 is n!, A000142
Row 2 is Latin squares, A002860
Row 3 is Latin cubes, A098679

So the array begins
1    2    6        24                120     720
1    2   12     576          161280
1    2   24 55296 2781803520
1    2

How does it continue, and is it in the OEIS? Ron? Brendan?

Best regards

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com

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