The recent proof of the Boij–Söderberg conjectures reveals new structure about Betti diagrams of modules, giving a complete description of the cone of Betti diagrams. We begin to expand on this new structure by investigating the semigroup of such diagrams. We prove that this semigroup is finitely generated, and answer several other fundamental questions about it.
"The semigroup of Betti diagrams." Algebra Number Theory 3 (3) 341 - 365, 2009. https://doi.org/10.2140/ant.2009.3.341