## Involution (Set)

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

For , 2, ..., the first few values of are 1, 2, 4, 10, 26, 76, ... (Sloane's A000085). The number of involutions on symbols cannot be expressed as a fixed number of hypergeometric terms (Petkovsek et al. 1996, p. 160).

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.

© 1996-9 Eric W. Weisstein
1999-05-26