YoungTableau ? YoungTableau -- an order of YoungTableaux

Synopsis

Operator: ?
Usage:

y1 ? y2
Inputs:
- y1, an instance of the type YoungTableau,
- y2, an instance of the type YoungTableau,
Outputs:
- a Boolean value, either "=", "<" or ">"

The order implemented checks where is the first row descent of the tableau. Then it applies lexicographical order to the coordinates of these cells.

If the row descent is in the same cell then the lexicographical order for the filling is outputted.

This order is implemented for th net of SpechtModuleElement so that the terms with some row descent appear last.

i1 : p = new Partition from {2,1}

o1 = Partition{2, 1}

o1 : Partition

i2 : y1 = youngTableau(p,{1,0,2})

o2 = | 1 0 |
     | 2 |

o2 : YoungTableau

i3 : y2 = youngTableau(p,{0,2,1})

o3 = | 0 2 |
     | 1 |

o3 : YoungTableau

i4 : y1 ? y2

o4 = >

o4 : Keyword

i5 : sort {y1,y2}

o5 = {| 0 2 |, | 1 0 |}
      | 1 |    | 2 |

o5 : List