2. For partitions of 7:

(i) generate all Ferrers diagrams using slide-and-float moves

(ii) use them to find P7,4 and P7,4

(iii) find P114 and list all corresponding partitions

Hint: Use Euler's conversion Pk Pn-kk To get Ferrers diagrams for 11, augment a column of 4 dots on the left to Ferrers diagrams of 7.

(iv) find the number of partitions of 11 with the largest part 4 and list all of them

Hint: These are conjugate to the partitions in (iii), their Ferrers diagrams are the transposes of those in (iii).