2 citations · 3 across the 9 of their papers we have counts for
9 papers
Prescribed Initial Behavior of
Reza Abdolmaleki, Shinya Kumashiro
It is well known that for every graded ideal , the numbers of minimal generators of its powers of are eventually increasing. However, its initial behavior can be su…
The Non-Pure Dual Exchange Property in Low Dimensions
Reza Abdolmaleki, Shinya Kumashiro
We investigate monomial ideals satisfying the non-pure dual exchange property, a notion introduced in connection with componentwise polymatroidal ideals. Our contributions are twof…
Defining ideals of Cohen-Macaulay fiber cones
Reza Abdolmaleki, Shinya Kumashiro
Let be a commutative Noetherian local ring with maximal ideal , and let be an ideal. The fiber cone is then an image of the polynomial ring over the residue f…
On the Betti numbers of monomial ideals and their powers
Reza Abdolmaleki, Rashid Zaare-Nahandi
Let the polynomial ring over a field . In this paper for some families of monomial ideals we study the minimal number of ge…
The saturation number of monomial ideals
Reza Abdolmaleki, Ali Akbar Yazdan Pour
Let be the polynomial ring over a field and be the irredundant maximal ideal of . For an ideal $I…
Toric ideals which are determinantal
Reza Abdolmaleki, Rashid Zaare-Nahandi
Given any equigenerated monomial ideal with the property that the defining ideal of the fiber cone of is generated by quadratic binomials, we introduce a matrix…
Certain monomial ideals whose numbers of generators of powers descend
Reza Abdolmaleki, Shinya Kumashiro
This paper studies the numbers of minimal generators of powers of monomial ideals in polynomial rings. For a monomial ideal in two variables, Eliahou, Herzog, and Saem gave a s…
On the initial behaviour of the number of generators of powers of monomial ideals
Reza Abdolmaleki, Jürgen Herzog, Rashid Zaare-Nahandi
Given a number , we construct a monomial ideal with the property that the function which describes the number of generators of has at least local maxima.
The saturation number of $\cb$-bounded stable monomial ideals and their powers
Reza Abdolmaleki, Jürgen Herzog, Guangjun Zhu
Let be the polynomial ring in variables over a field . In this paper, we compute the socle of $\cb$-bounded strongly stable ideals and determine that t…