1 citations · 1 across the 9 of their papers we have counts for
11 papers
Hierarchical filtrations of vector bundles and birational geometry
Rahim Rahmati-asghar
We introduce and systematically study \emph{hierarchical filtrations} of vector bundles on smooth projective varieties. These are filtrations by saturated subsheaves of equal rank…
Hierarchical filtrations of line bundles and optimal algebraic geometry codes
Rahim Rahmati-asghar
We introduce \emph{hierarchical depth}, a new invariant of line bundles and divisors, defined via maximal chains of effective sub-line bundles. This notion gives rise to \emph{hier…
On the polymatroidal property of monomial ideals with a view towards orderings of minimal generators
Somayeh Bandari, Rahim Rahmati-Asghar
We prove that a monomial ideal generated in a single degree, is polymatroidal if and only if it has linear quotients with respect to the lexicographical ordering of the minimal…
Expansion and contraction functors on matriods
Rahim Rahmati-Asghar
Let be a matroid. We study the expansions of mainly to see how the combinatorial properties of and its expansions are related to each other. It is shown that is a g…
Pretty -clean monomial ideals and -decomposable multicomplexes
Rahim Rahmati-Asghar
We introduce pretty -clean monomial ideals and -decomposable multicomplexes, respectively, as the extensions of the notions of -clean monomial ideals and -decomposable…
-clean monomial ideals
Rahim Rahmati-Asghar
In this paper, we introduce the concept of -clean monomial ideals as an extension of clean monomial ideals and present some homological and combinatorial properties of them. Usi…
On the facet ideal of an expanded simplicial complex
Somayeh Moradi, Rahim Rahmati-Asghar
For a simplicial complex , the affect of the expansion functor on combinatorial properties of and algebraic properties of its Stanley-Reisner ring has been studied in some p…
-shellable simplicial complexes and graphs
Rahim Rahmati-Asghar
In this paper we show that a -shellable simplicial complex is the expansion of a shellable complex. We prove that the face ring of a pure -shellable simplicial complex satisf…
On the Stanley-Reisner ideal of an expanded simplicial complex
Rahim Rahmati-Asghar, Somayeh Moradi
Let be a simplicial complex. We study the expansions of mainly to see how the algebraic and combinatorial properties of and its expansions are related to each other. It…
The behaviors of expansion functor on monomial ideals and toric rings
Rahim Rahmati-Asghar, Siamak Yassemi
In this paper we study some algebraic and combinatorial behaviors of expansion functor. We show that on monomial ideals some properties like polymatroidalness, weakly polymatroidal…
Cohen-Macaulay-ness in codimension for simplicial complexes and expansion functor
Rahim Rahmati-Asghar
In this paper we show that expansion of a Buchsbaum simplicial complex is , for an optimal integer . Also, by imposing extra assumptions on a simplicial compl…