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SkewTableau ++ SkewTableau -- direct sum of tableaux

Operator: ++
Usage:

T1 ++ T2
Inputs:
- T1, an instance of the type SkewTableau, a tableau.
- T2, an instance of the type SkewTableau, a tableau.
Outputs:
- S, an instance of the type SkewTableau, a direct sum of T1 and T2.

Description

The tableaux are combined into the disconnected components (not sharing an edge) of a single tableau.

i1 : T1 = skewTableau(new Partition from {5}, new Partition from {2})

             ┌───┬───┬───┐
o1 =         │   │   │   │
             └───┴───┴───┘

o1 : SkewTableau

i2 : T2 = skewTableau(new Partition from {3,2}, new Partition from {1}, {1,2,3,4})

         ┌───┬───┐
o2 =     │ 1 │ 2 │
     ┌───┼───┼───┘
     │ 3 │ 4 │    
     └───┴───┘    

o2 : SkewTableau

i3 : T1 ++ T2

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

o3 : SkewTableau

i4 : T2 ++ T1

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

o4 : SkewTableau

See also

components(SkewTableau) -- get the connected components of a tableau
SkewTableau || SkewTableau -- vertical concatenation of two tableaux

Ways to use this method:

SkewTableau ++ SkewTableau -- direct sum of tableaux

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Tableaux/documentation.m2:877:0.