Integer partitions

<< Combinatorica`
(* define a integer you want to investigate *)
n := 9
S[n_] := Partitions[n]
(* define the rank of a partition with the name "pr"*)
pr[s_] := Max[s] - Length[s]
(* partition statistics *)
Sort[Table[Mod[pr[s], 5], {s, S[n]}]]
(* list of paritions with rank *)
Do[Print[s, ", rank=", pr[s], "\[Congruent]",
  Mod[Max[s] - Length[s], 5], "(mod 5)"], {s, S[n]}]
(* you will see the partition statistics and list of paritions with \
rank *)