A096575 Number of fixed points of solid partitions under rotation operation.

1, 1, 1, 2, 2, 2, 4, 6, 6, 8, 11, 13, 17, 24, 28, 36, 47, 56, 69, 94, 114, 138, 177, 218, 262

Offset: 1

Author

Wouter Meeussen, Jun 27 2004

Keywords

• nonn
• hard
• more

Comments

Rotation has permutation cycle length 1 or 3. Uses function "solidformBTK" from link below.

Is this the same sequence as A002722? - R. J. Mathar, Sep 04 2008 [This still seems to be true even after 20 terms. - N. J. A. Sloane, Feb 05 2025]

Rotation of each of the plane partitions in a solid partition appears to lead to the same count of fixed points as rotating the 3D-partition as a whole. - Wouter Meeussen, Feb 05 2025

Examples

			Solid partition [{{3, 1, 1, 1}, {3}}, {{2, 1}}, {{1}}, {{1}}, {{1}}] rotates into [{{4, 1}, {1, 1}, {1, 1}}, {{2}, {1}}, {{1}}, {{1}}, {{1}}] by rotating each layer as a plane partition.
		

Links

• Wouter Meeussen, Mma functions for plane and solid partitions

Crossrefs

Cf. A000293, A094504, A094508, A096272, A096573, A096574, A096576, A096577, A096578, A096579, A096580, A096581, A119266.

Programs

Mathematica

Tr/@Table[Count[solidformBTK[par], arg_z /;turn[arg]==arg],{n,20}, {par, IntegerPartitions[n]}]

Extensions

a(16)-a(23) from Wouter Meeussen, Feb 05 2025

a(24)-a(25) from Wouter Meeussen, Jul 27 2025