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randomTabloid -- get a random tabloid

Usage:

randomTabloid(lam,mu)
Inputs:
- lam, an instance of the type Partition, the outer shape, $\lambda$, of T.
- mu, an instance of the type Partition, the inner shape, $\mu$, of T.
Outputs:
- T, an instance of the type Tabloid, a random tabloid with entries in $\{1,\ldots,N\}$, where $N$ is the length of $\lambda$. If $\mu$ is not provided, then it is assumed to be $0$.

Description

i1 : lam = new Partition from {5,4,3,3,1}

o1 = Partition{5, 4, 3, 3, 1}

o1 : Partition

i2 : mu = new Partition from {3,1,1}

o2 = Partition{3, 1, 1}

o2 : Partition

i3 : randomTabloid(lam,mu)

                    ┌─────────┐
o3 =                │ 6    4  │
          ┌─────────┴────┬────┘
          │ 7    9    2  │     
          ├─────────┬────┘     
          │ 3    1  │          
     ┌────┴─────────┤          
     │ 10   11   5  │          
     ├────┬─────────┘          
     │ 8  │                    
     └────┘                    

o3 : Tabloid

i4 : randomTabloid lam

     ┌────────────────────────┐
o4 = │ 7    4    9    12   2  │
     ├───────────────────┬────┘
     │ 8    16   6    14 │     
     ├──────────────┬────┘     
     │ 5    15   10 │          
     ├──────────────┤          
     │ 11   1    3  │          
     ├────┬─────────┘          
     │ 13 │                    
     └────┘                    

o4 : Tabloid

See also

randomSemistandardTableau -- get a random semistandard Young Tableau
randomStandardTableau -- get a random standard Young Tableau
allTabloids -- list all tabloids of a given shape

Ways to use randomTabloid:

randomTabloid(Partition)
randomTabloid(Partition,Partition)

For the programmer

The object randomTabloid is a method function.

The source of this document is in Tableaux/documentation.m2:1032:0.