# YoungTableau ? YoungTableau -- an order of YoungTableaux

## Synopsis

• Operator: ?
• Usage:
y1 ? y2
• Inputs:
• Outputs:
• , either "=", "<" or ">"

## Description

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