Bounds for the Multiplicity of Gorenstein algebras
  We prove upper bounds for the Hilbert-Samuel multiplicity of standard graded Gorenstein algebras. The main tool that we use is Boij-S\"oderberg theory to obtain a decomposition of the Betti table of a Gorenstein algebra as the sum of rational multiples of symmetrized pure tables. Our bound agrees with the one in the quasi-pure case obtained by Srinivasan [J. Algebra, vol.~208, no.~2, (1998)]. 
Sabine El Khoury and Manoj Kummini and Hema Srinivasan
math.AC