2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95098In this note we supply an elementary proof of the following well-known theorem of R. Stanley: the $h$-vectors of Gorenstein algebras of codimension 3 are SI-sequences, i.e. are symmetric and the first difference of their first half is an $O$-sequence.6 pages. Proc. of the A.M.S., to appearCommutative Algebra13E10 (Primary); 13H10 (Secondary)Stanley's theorem on codimension 3 Gorenstein $h$-vectorstext