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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 168646, 4900]*) (*NotebookOutlinePosition[ 169299, 4923]*) (* CellTagsIndexPosition[ 169255, 4919]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["inits", "Subsection"], Cell[BoxData[ \(<< DiscreteMath`Combinatorica`\)], "Input"], Cell[BoxData[ \(\(Clear[maxwords, residu, prune];\)\)], "Input"], Cell[BoxData[ \(\(residu[par : {1\ ... }, p_: 0] := p + Mod[Length[par], 2];\)\)], "Input"], Cell["\<\ (* corr 18/11/2012 13:38; not \"k< n-1 -(f-1) \" but \"k< l+1 -(f-1)\" *)\ \>", "Text"], Cell[BoxData[ \(residu[par_?PartitionQ, p_: 0] := Block[{f 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14, frontpar and tailpar are", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({Part[frontpar, \(-1\) + 14 - 1], Part[tailpar, \(-1\) + 14]}\)], "Input"], Cell[BoxData[ \({42, 45}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \({Part[frontpar, \(-1\) + 14 - 1], Part[tailpar, \(-1\) + 14]}\)], "Input"], Cell[BoxData[ \({17, 45}\)], "Output"] }, Open ]], Cell["\<\ and only unrankpartition[14,17] upto unrankpartition[14,PartitionsP[14]- 45] \ need to be calculated if frontpar and tailpar were known. I originally assumed that, apart from the tail end, the maxwords of \ partition[2n+1, k] was equal to partition[2n, k], but from n=14 onwords, \ this is not so. Below comes the calculation of 'tailpar' for partitions of n even and odd. But first: the variable ranges: { n , end of frontpart, start of tailpart, \ full length}\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Table[{n, \ Part[frontpar, \(-1\) + n - 1], PartitionsP[n] - Part[tailpar, \(-1\) + n], PartitionsP[n]}, {n, 3, 14}]\)], "Input"], Cell[BoxData[ \({{3, 1, 0, 3}, {4, 1, 1, 5}, {5, 3, 1, 7}, {6, 3, 3, 11}, {7, 8, 3, 15}, {8, 8, 8, 22}, {9, 15, 8, 30}, {10, 15, 21, 42}, {11, 30, 20, 56}, {12, 27, 47, 77}, {13, 45, 47, 101}, {14, 42, 90, 135}}\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["even # of parts", "Subsection"], Cell[BoxData[{ \(\(Table[maxwords /@ Partitions[n], {n, 2, 36, 2}];\)\), "\n", \(\(it = \(\((\(MatrixForm[First[#]]^Length[#] &\)\ /@ \ Split[#])\) &\) /@ %;\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Last[Last[#]] &\) /@ it\)], "Input"], Cell[BoxData[ \({2, 4, 8, 14, 21, 30, 45, 59, 76, 103, 127, 155, 197, 234, 275, 336, 388, 445}\)], "Output"] }, Open ]], Cell[BoxData[ \(\(tailpareven = %;\)\)], 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