proposition: Lemma cycle_type_eltr i : (i < n)%N -> cycle_typeSn (eltr n i) = hookpartn n.+1 1.
proof: Proof. move=> /inordi_neq_i1 Hi; rewrite /eltr; apply val_inj => /=. by rewrite /cycle_typeSn cycle_type_tperm // /partnCT cast_intpartnE card_ord. Qed.
imports: mathcomp(all_ssreflect) mathcomp(fingroup perm ssralg morphism perm action) mathcomp(zmodp) mathcomp(vector matrix mxalgebra ssrnum algC) mathcomp(mxrepresentation classfun character) permcomp tools partition congr cycles cycletype presentSn