A263921 Number of multisets of n permutations of [n] with the symmetric group acting on the permutation elements.

1, 1, 2, 10, 762, 1876255, 274382326290, 3265588553925722827, 4299566944396584777543664576, 828675148077536475804944305151462053905, 30068353582978459601855528390398866877243129478172220

Offset: 0

Author

Marko Riedel, Oct 29 2015

Keywords

• nonn

Comments

The Harary and Palmer text has the generic formulas for power group enumeration.

a(n) is also the number of preference profiles with n alternatives and n agents (IANC model). Egecioglu (2009) contains a general formula. - Alexander Karpov, Dec 15 2017

Row-latin squares distinct up to row/column permutation, with application to the Stable Marriage Problem representing distinct Men's or Women's preference profiles. - Dan Eilers, May 18 2025

Examples

			See linked examples.
		

References

• F. Harary and E. Palmer, Graphical Enumeration, Academic Press, NY, 1973.

Links

• Ö. Egecioglu, Uniform generation of anonymous and neutral preference profiles for social choice rules, UC Santa Barbara Report 2005-25.
• Ö. Egecioglu, Uniform generation of anonymous and neutral preference profiles for social choice rules, Monte Carlo Methods and Applications, 15(3), Jan 2009, 241-255.
• Dan Eilers, Examples for n=3, n=4
• Marko R. Riedel, Combinatorial counting with symmetry
• Marko Riedel, Maple implementation of Power Group Enumeration

Crossrefs

A123234 (reduced latin squares up to row/column permutation).