Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 PosetToTableau

Source Notebook

Convert a partially ordered set of coordinates to a Young tableau

Contributed by: Ed Pegg Jr

ResourceFunction["PosetToTableau"][poset]

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

Details

A poset is a partially ordered set of coordinates.

Examples

Basic Examples (2) 

Convert a poset into a Young tableau:

In[1]:=
ResourceFunction[ "PosetToTableau"][{{1, 1}, {1, 2}, {2, 1}, {1, 3}, {3, 1}, {2, 2}, {3, 2}, {1, 4}, {4, 1}}]
Out[1]=

The resource function TableauToPoset recovers the original poset:

In[2]:=
ResourceFunction["TableauToPoset"][%]
Out[2]=

Scope (2) 

Enumerate all Young tableaux of shape (4,2), and convert them into posets:

In[3]:=
young = ResourceFunction["StandardYoungTableaux"][{4, 2}]; posets = ResourceFunction["TableauToPoset"] /@ young
Out[4]=

Convert these posets to Young tableaux:

In[5]:=
tableau = ResourceFunction["PosetToTableau"] /@ posets
Out[5]=

Check the back and forth conversion:

In[6]:=
tableau === young
Out[6]=

Generate a random sampling of Young tableaux, and convert them to posets:

In[7]:=
large = ResourceFunction["RandomYoungTableau"][{5, 4, 2, 2}, 5]; posetsl = ResourceFunction["TableauToPoset"] /@ large
Out[8]=

Convert these posets to Young tableaux:

In[9]:=
tableaux = ResourceFunction["PosetToTableau"] /@ posetsl
Out[9]=

Check the back and forth conversion:

In[10]:=
large === tableaux
Out[10]=

Version History

  • 1.0.0 – 28 February 2022

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