An involution of a Set is a Permutation of which does not contain any cycles of length .
The Permutation Matrices of an involution are Symmetric.
The number of involutions of a Set containing the first integers is given by the Recurrence
Relation
See also Permutation
References
Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A. K. Peters, 1996.
Ruskey, F. ``Information on Involutions.''
http://sue.csc.uvic.ca/~cos/inf/perm/Involutions.html.
Sloane, N. J. A. Sequence
A000085/M1221
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.