I was asked to investigate this question and to present my findings and I would like some sense of help and direction, I am very lost:-(
2n people, all of different heights
How many ways are there to order them such that
--- There are exactly 2 rows --- All the heights increase from left to right --- The people in the back row have to be taller than the person immediately in front of them in the first row
Does anyone know of a recurrence relation that there is for this question, or any explicit formulas that I can investigate?
I have worked it for 2n = 6, and have found that in terms of Young Tableaux if we use the equation $\frac{(2n)!}{\prod(Hook's Numbers)}$ we achieve the answer 5, which is also what I got when doing it by hand.
Now I am wondering as to how I would prove this