“Involution (Set)”的概念、定义、习题解题方法及翻译-数学辞典

单词

Involution (Set)

释义

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 RecurrenceRelation

For

, 2, ..., the first few values of

are 1, 2, 4, 10, 26, 76, ... (Sloane's A000085). The number ofinvolutions 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. SequenceA000085/M1221in ``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.

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