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                    Mathematica-Compatible Notebook

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Cell["\<\
it would be nice to count trees ofver all forrests, \
{1,0}=1,{1,1,0,0}=2,{1,0,1,0}=3,{1,1,1,0,0,0}=4 etc..
             NOW DONE !!\
\>", "Text"],

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Cell["RankTree", "Subsection"],

Cell["the Catalan Triangle :", "Text"],

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Cell["\<\
this does a \"TransposePartition\" of a non-decreasing list, viewed as a \
Ferrers Diagram: function\" trapo\"\
\>", "Text"],

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\>", "Input",
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NthTree[w_Integer/;(w>0),o_Integer:1]:=Module[{temp1,temp2},
temp1=NthTree1[w,o];
temp2=Prepend[temp1,0]+Range[Length[temp1]+1]; MapAt[#+1&,0*Range[2 \
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\>", "Input",
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NthTree[w_Integer/;(w>0),o_Integer:1]:=Module[{temp1,temp2},
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temp1=NthTree1[w2,o2];
temp2=Prepend[temp1,0]+Range[Length[temp1]+1]; MapAt[#+1&,0*Range[2 \
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\>", "Input",
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Cell["\<\
the function NthTree1 produces the y-coordinates of a chessboard rook path, \
to be surrounded with obligatory {0, ---- , 1}\
\>", "Text"],

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NthTree[ integer] gives the nth tree of the forrest just large enough to hold \
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\>", "Text"],

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and optional second argument allows a minimal forrest size to be specified.\
\>", "Text"],

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cattria[100,100]-7
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\>", "Input"],

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