Expansions of monomial ideals and multigraded modules
  We introduce an exact functor defined on multigraded modules which we call the expansion functor and study its homological properties. The expansion functor applied to a monomial ideal amounts to substitute the variables by monomial prime ideals and to apply this substitution to the generators of the ideal. This operation naturally occurs in various combinatorial contexts. 
Shamila Bayati, J\"urgen Herzog
math.AC