عنوان مجله
|
COMMUNICATIONS IN ALGEBRA
|
چکیده
|
In this article, we study some algebraic and combinatorial behaviors of expansion
functor. We show that on monomial ideals some properties like polymatroidalness,
weakly polymatroidalness, and having linear quotients are preserved under taking the
expansion functor.
The main part of the article is devoted to study of toric ideals associated to the
expansion of subsets of monomials which are minimal with respect to divisibility. It
is shown that, for a given discrete polymatroid P, if toric ideal 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’s conjecture is preserved under taking the expansion
functor. Finally, the construction of Gröbner bases and some homological properties of
toric ideals associated to expansions of subsets of monomials is investigated.
|