Stacks of algebras and their homology
  For any increasing function $f: {\Bbb N} \rightarrow {\Bbb N}_{\ge 2}$ which takes only finitely many distinct values, a connected finite dimensional algebra $\Lambda$ is constructed, with the property that $\text{fin.dim}_n\, \Lambda = f(n)$ for all $n$; here $\text{fin.dim}_n\, \Lambda$ is the $n$-generated finitistic dimension of $\Lambda$. The stacking technique developed for this construction of homological examples permits strong control over the higher syzygies of $\Lambda$-modules in terms of the algebras serving as layers. 
Nancy Heinschel and Birge Huisgen-Zimmermann
math.RA math.RT