Tabloid -- a type of HashTable representing a Young tabloid

Description

An object of type Tabloid is a subclass of type YoungTableau. A tabloid represents an equivalence class of Young tableaux, with entries in $\{1,\ldots,n\}$. Two tabloids are equal if they have the same shape, and each corresponding row contains the same boxes, up to some permutation. Hence, rows are drawn without dividing boxes.

i1 : lam = new Partition from {4,3,2}

o1 = Partition{4, 3, 2}

o1 : Partition

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

o2 = Partition{3, 1}

o2 : Partition

i3 : T = tabloid(lam,mu,{1,2,5,3,4})

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

o3 : Tabloid

i4 : T' = tabloid(lam,mu,{1,5,2,3,4})

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

o4 : Tabloid

i5 : T == T'

o5 = true

Functions and methods returning an object of class Tabloid:

randomTabloid -- get a random tabloid
representative -- get a canonical representative of a tabloid
tabloid -- constructor for type Tabloid

Methods that use an object of class Tabloid:

representative(Tabloid) -- see representative -- get a canonical representative of a tabloid
Tabloid == Tabloid -- check if two tabloids are equal
toList(Tabloid) -- list representation of a tabloid
youngTableau(Tabloid) -- see youngTableau -- constructor for type YoungTableau

For the programmer

The object Tabloid is a type, with ancestor classes YoungTableau < HashTable < Thing.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Tableaux/documentation.m2:59:0.

Tabloid -- a type of HashTable representing a Young tabloid

Description

See also

Functions and methods returning an object of class Tabloid:

Methods that use an object of class Tabloid:

For the programmer