info prev up next book cdrom email home

Involution (Set)

An involution of a Set $S$ is a Permutation of $S$ which does not contain any cycles of length $>2$. The Permutation Matrices of an involution are Symmetric. The number of involutions $I(n)$ of a Set containing the first $n$ integers is given by the Recurrence Relation


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

See also Permutation


Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A. K. Peters, 1996.

Ruskey, F. ``Information on Involutions.''

Sloane, N. J. A. Sequence A000085/M1221 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein