Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 TableauToPoset

Source Notebook

Convert a Young tableau to a partially ordered set of coordinates

Contributed by: Ed Pegg Jr

ResourceFunction["TableauToPoset"][young]

converts the Young tableau young to a partially ordered set of coordinates.

Details

A poset is a partially ordered set of coordinates.

Examples

Basic Examples (3) 

All Young tableaux of shape (3,2):

In[1]:=
young = ResourceFunction["StandardYoungTableaux"][{3, 2}]
Out[1]=

Convert the Young tableaux to posets:

In[2]:=
posets = ResourceFunction["TableauToPoset"] /@ young
Out[2]=

Show the Young tableaux with their corresponding poset diagrams:

In[3]:=
Row[Column /@ Transpose[{ Style[ Grid[Map[Function[i, Item[i, Frame -> True]], Reverse[#], {2}]], 24] & /@ young, Graphics[{Arrowheads[Medium], Arrow /@ Partition[#, 2, 1]} ] & /@ posets}], Spacer[20]]
Out[3]=

Scope (2) 

A random sampling of Young tableaux:

In[4]:=
large = ResourceFunction["RandomYoungTableau"][{5, 4, 2, 2}, 5]
Out[4]=

Young tableaux shown with poset diagrams:

In[5]:=
Row[Column /@ Transpose[{ Grid[Map[Function[i, Item[i, Frame -> True]], Reverse[#], {2}]] & /@ large, Graphics[{Arrowheads[Medium], Arrow /@ Partition[ResourceFunction["TableauToPoset"]@#, 2, 1]} ] & /@ large}], Spacer[20]]
Out[5]=

Version History

  • 1.0.0 – 14 February 2022

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