Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
PeterBurbery`Combinatorics`
TableauToPoset  |
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Details and Options
Examples
(2)
Basic Examples
(1)
All Young tableaux of shape (3,2):
In[1]:=
young=
[{3,2}]
 | StandardYoungTableaux |
Out[1]=
{{{1,2,3},{4,5}},{{1,2,4},{3,5}},{{1,2,5},{3,4}},{{1,3,4},{2,5}},{{1,3,5},{2,4}}}
Convert the Young tableaux to posets:
In[2]:=
posets=
/@young
| TableauToPoset |
Out[2]=
{{{1,1},{2,1},{3,1},{1,2},{2,2}},{{1,1},{2,1},{1,2},{3,1},{2,2}},{{1,1},{2,1},{1,2},{2,2},{3,1}},{{1,1},{1,2},{2,1},{3,1},{2,2}},{{1,1},{1,2},{2,1},{2,2},{3,1}}}
Show the Young tableaux with their corresponding poset diagrams:
In[3]:=
Row[Column/@Transpose[{Style[Grid[Map[Function[i,Item[i,FrameTrue]],Reverse[#],{2}]],24]&/@young,Graphics[{Arrowheads[Medium],Arrow/@Partition[#,2,1]}]&/@posets}],Spacer[20]]
Out[3]=
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Scope
(1)
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""