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

Synopsis

Function: firstRowDescent
Usage:

firstRowDescent y
Inputs:
- y, an instance of the type YoungTableau,
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

Ways to use this method: