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YoungTableau || YoungTableau -- vertical concatenation of two tableaux

Operator: ||
Usage:

T1 || T2
Inputs:
- T1, an instance of the type YoungTableau, a tableau.
- T2, an instance of the type YoungTableau, a tableau.
Outputs:
- S, an instance of the type YoungTableau, a single tableau with T1 directly above T2.

Description

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

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

o1 : YoungTableau

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

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

o2 : YoungTableau

i3 : T1 || T2

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

o3 : YoungTableau

i4 : T2 || T1

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

o4 : YoungTableau

See also

verticalConcatenate -- vertical concatenation of a list of tableaux
YoungTableau ++ YoungTableau -- direct sum of tableaux

Ways to use this method:

YoungTableau || YoungTableau -- vertical concatenation of two tableaux

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Tableaux/documentation.m2:2001:0.