2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61492We give three determinantal expressions for the Hilbert series as well as the Hilbert function of a Pfaffian ring, and a closed form product formula for its multiplicity. An appendix outlining some basic facts about degeneracy loci and applications to multiplicity formulae for Pfaffian rings is also included.20 pages, AmS-LaTeXCommutative AlgebraAlgebraic GeometryCombinatorics13C40 (Primary) 05A15 05A19 13C40 13F55 13H10 13H15 14C17 (Secondary)text