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In this paper we study some algebraic and combinatorial behaviors ofexpansion functor. We show that on monomial ideals some properties likepolymatroidalness, weakly polymatroidalness and having linear quotients arepreserved under taking the expansion functor.  The main part of the paper is devoted to study of toric ideals associated tothe expansion of subsets of monomials which are minimal with respect todivisibility. It is shown that, for a given discrete polymatroid $P$, if toricideal of $P$ is generated by double swaps then toric ideal of any expansion of$P$ has such a property. This result, in a special case, says that White'sconjecture is preserved under taking the expansion functor. Finally, theconstruction of Gr\"{o}bner bases and some homological properties of toricideals associated to expansions of subsets of monomials is investigated.

The behaviors of expansion functor on monomial ideals and toric rings