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A096575
Number of fixed points of solid partitions under rotation operation.
9
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]
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}]
KEYWORD
more,nonn
AUTHOR
Wouter Meeussen, Jun 27 2004
STATUS
approved