Actually, the element deleted is replaced by by infinity in that cell of the Young Tableau. And, then we perform an operation called Youngify(Y, i, j) where Y is the 2D-Young matrix, i and j are the coordinates of the element deleted.
This function sets the blank/infinity created by the deletion of the element in its proper position by rearranging the Young Tableau much like the heapify procedure.
Please refer this PDF which contains the details - https://lyle.smu.edu/~saad/courses/cse3358/ps5/problemset5sol.pdf
The blank/infinity is compared with the immediate right and immediate bottom element each time and the smallest is exchanged with it out of the 2. This procedure ultimately arranges all the elements in their correct position.
Eg :- Youngify on position Y[1, 1] :- The position Y[1, 1] = INF, is compared with position Y[1, 2] = 2 and position Y[2, 1] = 3, the smaller one is Y[1, 2] is exchanged with Y[1, 1] and now Y[1, 2] becomes INF. Now same procedure is repeated for Y[1, 2] and so on..
2 4 5 14
3 6 18 23
10 12 25 oo
31 oo oo oo