proposition: Lemma symh_syms_partdom mu : 'h[mu] = 's[mu] + \sum_(la | (mu < la :> 'PDom_d)%O) 'K(la, mu) *: 's[la] :> SF.
proof: Proof. rewrite -(map_symh_prod intr) symh_syms_partdom_int. rewrite rmorphD rmorph_sum /= map_syms; congr (_ + _); apply eq_bigr => i _. rewrite linearZ_LR /= map_syms /=; congr (_ *: _). by rewrite mulrz_nat. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(ssralg ssrint fingroup perm) mathcomp(ssrcomplements freeg mpoly) sorted tools ordtype permuted partition skewpart composition Yamanouchi std tableau stdtab skewtab permcent antisym Schur_mpoly therule Schur_altdef unitriginv