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For any positive integer n we denote by lambda(n) the unique integer such that n = 2(lambda(n)) c, where c is odd.

In the paper we prove that a permutation sigma of [1, n] with orbits O-1,..., O-m O m is a self-complementing permutation of a k-uniform hypergraph of order n if and only if there is an integer l >= 0 such that k = a2(l) + s, a is odd, 0 <= s <= 2(l) and the following two conditions hold:

(i)n = b2(l+1) + r,r is an element of {0,..., 2(l) - 1 + s}, and

(ii) Sigma(i:lambda(vertical bar Oi vertical bar)<= l) vertical bar O-i vertical bar <= r.

For k = 2 this result is the very well known characterization of self-complementing permutation of graphs given by Ringel and Sachs.

Cited literature [7 references]

https://hal.inria.fr/hal-00988180

Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>

Submitted on : Wednesday, May 7, 2014 - 4:08:12 PM

Last modification on : Thursday, October 4, 2018 - 10:12:02 PM

Long-term archiving on: : Thursday, August 7, 2014 - 11:31:30 AM

Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>

Submitted on : Wednesday, May 7, 2014 - 4:08:12 PM

Last modification on : Thursday, October 4, 2018 - 10:12:02 PM

Long-term archiving on: : Thursday, August 7, 2014 - 11:31:30 AM