randomSemistandardTableau -- get a random semistandard Young Tableau

Usage:

randomSemistandardTableau(lam,mu,N)
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.
- N, an integer, the maximum entry.
Outputs:
- T, an instance of the type YoungTableau, a random semistandard Young tableau with entries in $\{1,\ldots,N\}$. If $N$ is not provided, then it is assumed to be the length of $\lambda$. If $\mu$ is not provided, then it is assumed to be $0$.

Description

Note that this does not select a tableau uniformly randomly.

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 : randomSemistandardTableau(lam,mu)

                 ┌───┬───┐
o3 =             │ 3 │ 5 │
         ┌───┬───┼───┼───┘
         │ 1 │ 3 │ 5 │    
         ├───┼───┼───┘    
         │ 2 │ 4 │        
     ┌───┼───┼───┤        
     │ 3 │ 3 │ 5 │        
     ├───┼───┴───┘        
     │ 4 │                
     └───┘                

o3 : YoungTableau

i4 : randomSemistandardTableau lam

     ┌───┬───┬───┬───┬───┐
o4 = │ 1 │ 1 │ 2 │ 3 │ 5 │
     ├───┼───┼───┼───┼───┘
     │ 2 │ 3 │ 3 │ 4 │    
     ├───┼───┼───┼───┘    
     │ 3 │ 4 │ 4 │        
     ├───┼───┼───┤        
     │ 4 │ 5 │ 5 │        
     ├───┼───┴───┘        
     │ 5 │                
     └───┘                

o4 : YoungTableau

Ways to use randomSemistandardTableau:

randomSemistandardTableau(Partition)
randomSemistandardTableau(Partition,Partition)
randomSemistandardTableau(Partition,Partition,ZZ)
randomSemistandardTableau(Partition,ZZ)

For the programmer

The object randomSemistandardTableau is a method function.

The source of this document is in Tableaux/documentation.m2:973:0.

randomSemistandardTableau -- get a random semistandard Young Tableau

Description

See also

Ways to use randomSemistandardTableau:

For the programmer