A071608 Number of complete mappings f(x) of Z_{2n+1} such that -(-id+f)^(-1)=f.

1, 1, 0, 4, 0, 0, 80, 48, 0, 3328, 1920, 0, 270080, 131328, 0, 3257736, 16379904, 0, 5750476800, 2942582784, 0, 1376249266176, 706948005888, 0, 430415593603072

Offset: 0

Author

J. Hsiang, D. F. Hsu and Y. P. Shieh (arping(AT)turing.csie.ntu.edu.tw), Jun 03 2002

Keywords

• nonn

Comments

A complete mapping of a cyclic group (Zn,+) is a permutation f(x) of Zn such that f(0)=0 and that f(x)-x is also a permutation.

Examples

			f(x)=3x in (Z_7,+) is a complete mapping of Z_7 since f(0)=0 and f(x)-x (=2x) is also a permutation of Z_7. And -(-id+f)^(-1)(x)=f(x).
		

References

• Y. P. Shieh, "Partition strategies for #P-complete problems with applications to enumerative combinatorics", PhD thesis, National Taiwan University, 2001.
• Y. P. Shieh, J. Hsiang and D. F. Hsu, "On the enumeration of Abelian k-complete mappings", vol. 144 of Congressus Numerantium, 2000, pp. 67-88.

Links

• Y. P. Shieh, Cyclic complete mappings counting problems

Crossrefs

Cf. A003111.