# firstRowDescent(YoungTableau) -- retrieves the first row descent of a young tableau

## Synopsis

• Function: firstRowDescent
• Usage:
firstRowDescent y
• Inputs:
• Outputs:
• a, an integer, the row of the row descent or -1 if there is no row descent
• b, an integer, the column of the row descent or -1 if there is no row descent

## Description

A row descent is defined to be a cell (a,b) in a tableau $T$ such that T_(a,b)>T_(a,b+1). This method reads by columns from left to right and each column is read from the top down until the first row descent is found. If no row descent is found the pair (a,b)= (-1,-1) is returned.

 i1 : p = new Partition from {3,2,1} o1 = Partition{3, 2, 1} o1 : Partition i2 : y = youngTableau(p,{1,2,3,5,4,6}) o2 = | 1 2 3 | | 5 4 | | 6 | o2 : YoungTableau i3 : firstRowDescent y o3 = (1, 0) o3 : Sequence i4 : y2 = youngTableau(p,{1,2,4,3,5,6}) o4 = | 1 2 4 | | 3 5 | | 6 | o4 : YoungTableau i5 : firstRowDescent y2 o5 = (-1, -1) o5 : Sequence