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

1,4

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

Links

Table of n, a(n) for n=1..25.

Wouter Meeussen, Mma functions for plane and solid partitions

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A264869 A292728 A365719 * A002722 A261610 A265251

Adjacent sequences: A096572 A096573 A096574 * A096576 A096577 A096578

Keyword

nonn,hard,more

Author

Wouter Meeussen, Jun 27 2004

Extensions

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

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

Status

approved