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

Offset

1,4

Comments

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

Is this the same sequence as A002722? [From R. J. Mathar, Sep 04 2008]

Links

Table of n, a(n) for n=1..15.

Wouter Meeussen, Solid Partitions Mathematica functions

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

turn[par_List] := Module[{maks, wide, it}, wide = Length[par[[1]]]; maks = Max[Length[par], wide, Flatten[par]]; it = Join[ #, Table[0, {wide - Length[ # ]}]] & /@( par /. i_Integer :> Table[If[w > i, 0, 1], {w, maks}]); DeleteCases[DeleteCases[Transpose[Apply[Plus, it, 1]], 0 | {}, -1], 0|{}, -1]]; Table[sn =Sort@Flatten[solidformBTK /@ Partitions[n]]; Frequencies[Length /@ ToCycles[Ordering[Map[turn @ # &, sn, {2}]]] ], {n, 1, 15}]

Crossrefs

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

Sequence in context: A264869 A292728 A365719 * A002722 A261610 A265251

Adjacent sequences: A096572 A096573 A096574 * A096576 A096577 A096578

Keyword

more,nonn

Author

Wouter Meeussen, Jun 27 2004

Status

approved