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A096575
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Number of fixed points of solid partitions under rotation operation.
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9
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1, 1, 1, 2, 2, 2, 4, 6, 6, 8, 11, 13, 17, 24, 28
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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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 (mathar(AT)strw.leidenuniv.nl), Sep 04 2008]
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LINKS
| Wouter Meeussen, Solid Partitions Mathematica functions
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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.
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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}]
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CROSSREFS
| Cf. A000293, A094504, A094508, A096272, A096573, A096574, A096576, A096577, A096578, A096579, A096580, A096581.
Sequence in context: A170887 A103265 A008238 * A002722 A093393 A090858
Adjacent sequences: A096572 A096573 A096574 * A096576 A096577 A096578
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KEYWORD
| more,nonn
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 27 2004
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