I have a problem which is mostly neatly described by using Young Tableaux. Mathematica seems to have these Tableaux built in, except that the Tableaux
function is only in Combinatorica. When I Needs[Combinatorica]
I get a warning suggesting that I look at the Compatability Guide for Combinatorica, which I can't seem to find. Does anyone have a link, or know if any of the Tableaux
-related functions are the problematic ones?
The Tableaux function itself is hardly documented at all, and its output is quite tough to read. I am hoping there is a nice built-in way to draw the Tableaux in the nice YT in English notation (longest rows on top) [A custom drawing function is in How to insert a function into OptionsPattern? ]. Is there such a function?
Finally, can anyone explain what the format of the input to Tableaux
should be?
Here are some examples that work:
In[1]:= Needs["Combinatorica`"]
General::compat: Combinatorica Graph and Permutations functionality has been superseded by
preloaded functionality. The package now being loaded may conflict with this. Please see
the Compatibility Guide for details.
In[2]:= Tableaux[3]
Out[2]= {{{1, 2, 3}}, {{1, 3}, {2}}, {{1, 2}, {3}}, {{1}, {2}, {3}}}
In[3]:= Tableaux[{3}]
Out[3]= {{{1, 2, 3}}}
In[4]:= Tableaux /@ IntegerPartitions[3]
Out[4]= {{{{1, 2, 3}}}, {{{1, 3}, {2}}, {{1,
2}, {3}}}, {{{1}, {2}, {3}}}}
while something like Tableaux[{1, 2, 3}]
gives errors.
Does Tableaux[integer]
give all possible tableaux with integer
entries?
Does Tableaux[{int1, int2, ..., intk}]
give all possible tableaux of k
rows of length int1
... intk
respectively? This would explain why Tableaux[{1,2,3}]
throws errors---it would be a malformed tableaux.