columnStabilizer -- the column stabilizer of a tableau

Usage:

columnStabilizer T
Inputs:
- T, an instance of the type YoungTableau, a tableau.
Outputs:
- l, a list, the permutations in the column stabilizer.

Description

A permutation acts on a tableau by permuting its entries. The column stabilizer of a tableau is the group of permutations that leave boxes in their original columns.

i1 : T = youngTableau(new Partition from {2,2,1}, {1,4,2,5,3})

     ┌───┬───┐
o1 = │ 1 │ 4 │
     ├───┼───┤
     │ 2 │ 5 │
     ├───┼───┘
     │ 3 │    
     └───┘    

o1 : YoungTableau

i2 : columnStabilizer T

o2 = {Permutation{1, 2, 3, 4, 5}, Permutation{1, 2, 3, 5, 4}, Permutation{1,
     ------------------------------------------------------------------------
     3, 2, 4, 5}, Permutation{1, 3, 2, 5, 4}, Permutation{2, 1, 3, 4, 5},
     ------------------------------------------------------------------------
     Permutation{2, 1, 3, 5, 4}, Permutation{2, 3, 1, 4, 5}, Permutation{2,
     ------------------------------------------------------------------------
     3, 1, 5, 4}, Permutation{3, 1, 2, 4, 5}, Permutation{3, 1, 2, 5, 4},
     ------------------------------------------------------------------------
     Permutation{3, 2, 1, 4, 5}, Permutation{3, 2, 1, 5, 4}}

o2 : List

Ways to use columnStabilizer:

columnStabilizer(YoungTableau)

For the programmer

The object columnStabilizer is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Tableaux/documentation.m2:388:0.

columnStabilizer -- the column stabilizer of a tableau

Description

See also

Ways to use columnStabilizer:

For the programmer