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representative -- get a canonical representative of a tabloid

Usage:

representative T
Inputs:
- T, an instance of the type Tabloid, a tabloid.
Outputs:
- T', an instance of the type YoungTableau, a representative of T.

Description

A tabloid is an equivalence class of Young Tableaux. We can obtain a canonical representative by sorting the boxes in each row.

i1 : T = tabloid(new Partition from {6,3,2}, new Partition from {2}, {9,5,1,2,4,3,7,8,6})

             ┌───────────────┐
o1 =         │ 9   5   1   2 │
     ┌───────┴───┬───────────┘
     │ 4   3   7 │            
     ├───────┬───┘            
     │ 8   6 │                
     └───────┘                

o1 : Tabloid

i2 : representative T

             ┌───┬───┬───┬───┐
o2 =         │ 1 │ 2 │ 5 │ 9 │
     ┌───┬───┼───┼───┴───┴───┘
     │ 3 │ 4 │ 7 │            
     ├───┼───┼───┘            
     │ 6 │ 8 │                
     └───┴───┘                

o2 : YoungTableau

See also

Tabloid -- a type of HashTable representing a Young tabloid

Ways to use representative:

representative(Tabloid)

For the programmer

The object representative is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Tableaux/documentation.m2:1079:0.