Function Repository Resource:

# TableauQ

Determine if a list of values forms a Young tableau

Contributed by: Ed Pegg Jr and Steven Skiena
 ResourceFunction["TableauQ"][t] determines if t is a Young tableau.

## Details

A Young tableau is a list of lists of decreasing length partitioning a permutation. For all entries in a Young tableau, t[[a,b]]<t[[a+1,b]] and t[[a,b]]<t[[a,b+1]].
Young tableaux are often called tableaux.
A few pictures for items related to Young tableaux:
 Young diagram of Young tableau {{1,2,4},{3,5}}, English notation Young diagram of Young tableau {{1,2,4},{3,5}}, French notation Ferrers diagrams of Young tableau {{1,2,4},{3,5}} {{1,2,4},{3,5}} Young tableau

## Examples

### Basic Examples (1)

Check a simple tableau:

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### Scope (2)

Create a random pair of order 15 tableaux:

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Verify these are each a tableau:

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This is not a tableau:

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### Applications (1)

All 6! tableaux pairs generated from order 6 permutations are verified as being tableaux:

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## Version History

• 1.0.0 – 24 January 2022