allStandardTableaux -- list all standard Young tableaux of a given shape

Usage:

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

Description

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

o1 = -*a bagged sequence of length 70*-

o1 : Bag

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

The function numStandardTableaux computes the number of SYT.

i3 : # theBag

o3 = 70

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

o4 = 70

Ways to use allStandardTableaux:

allStandardTableaux(Partition)

For the programmer

The object allStandardTableaux is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Tableaux/documentation.m2:168:0.

allStandardTableaux -- list all standard Young tableaux of a given shape

Description

See also

Ways to use allStandardTableaux:

For the programmer