allTabloids -- list all tabloids of a given shape

Usage:

allSemistandardTableaux(lam,mu)
Inputs:
- lam, an instance of the type Partition, the outer shape, $\lambda$.
- mu, an instance of the type Partition, the inner shape, $\mu$.
Outputs:
- b, a bag, bagged list of all tabloids of given shape and entries in $\{1,\ldots,N\}$, where $N$ is the size of the tabloid.

Description

i1 : theBag = allTabloids(new Partition from {4,3,1})

o1 = -*a bagged sequence of length 280*-

o1 : Bag

i2 : for i from 0 to 4 do print theBag#i
┌───────────────┐
│ 1   2   3   4 │
├───────────┬───┘
│ 5   6   7 │    
├───┬───────┘    
│ 8 │            
└───┘            
┌───────────────┐
│ 1   2   3   4 │
├───────────┬───┘
│ 5   6   8 │    
├───┬───────┘    
│ 7 │            
└───┘            
┌───────────────┐
│ 1   2   3   4 │
├───────────┬───┘
│ 5   7   8 │    
├───┬───────┘    
│ 6 │            
└───┘            
┌───────────────┐
│ 1   2   3   4 │
├───────────┬───┘
│ 6   7   8 │    
├───┬───────┘    
│ 5 │            
└───┘            
┌───────────────┐
│ 1   2   3   5 │
├───────────┬───┘
│ 4   6   7 │    
├───┬───────┘    
│ 8 │            
└───┘

The function numTabloids computes the number of tabloids.

i3 : # theBag

o3 = 280

i4 : numTabloids(new Partition from {4,3,1})

o4 = 280

Ways to use allTabloids:

allTabloids(Partition)
allTabloids(Partition,Partition)

For the programmer

The object allTabloids is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Tableaux/documentation.m2:228:0.

allTabloids -- list all tabloids of a given shape

Description

See also

Ways to use allTabloids:

For the programmer