22 citations · 26 across the 5 of their papers we have counts for
12 papers
Semi-regular sequences and other random systems of equations
M. Bigdeli, E. De Negri, M. M. Dizdarevic +3
The security of multivariate cryptosystems and digital signature schemes relies on the hardness of solving a system of polynomial equations over a finite field. Polynomial system s…
Multigraded minimal free resolutions of simplicial subclutters
Mina Bigdeli, Ali Akbar Yazdan Pour
This paper concerns the study of a class of clutters called simplicial subclutters. Given a clutter and its simplicial subclutter , we compare some algeb…
Edge ideals with almost maximal finite index and their powers
Mina Bigdeli
A graded ideal in , where is a field, is said to have almost maximal finite index if its minimal free resolution is linear up to the ho…
Decomposable clutters and a generalization of Simon's conjectutre
Mina Bigdeli, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi
Each (equigenerated) squarefree monomial ideal in the polynomial ring represents a family of subsets of , called a (uniform) clutter. In this…
Chordality, -collapsibility, and componentwise linear ideals
Mina Bigdeli, Sara Faridi
Using the concept of -collapsibility from combinatorial topology, we define chordal simplicial complexes and show that their Stanley-Reisner ideals are componentwise linear. Our…
Simplicial orders and chordality
Mina Bigdeli, Jürgen Herzog, Ali Akbar Yazdan Pour +1
Chordal clutters in the sense of [14] and [3] are defined via simplicial orders. Their circuit ideal has a linear resolution, independent of the characteristic of the base field. W…
Isotonian Algebras
Mina Bigdeli, Jürgen Herzog, Takayuki Hibi +2
To a pair and of finite posets we attach the toric ring whose generators are in bijection to the isotone maps from to . This class of algebras, called isoto…
Stability of Betti numbers under reduction processes: towards chordality of clutters
Mina Bigdeli, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi
For a given clutter , let be the circuit ideal in the polynomial ring . In this paper, we show that the Betti numbers of and $I + (…
Toric rings, inseparability and rigidity
Mina Bigdeli, Jürgen Herzog, Dancheng Lu
This article provides the basic algebraic background on infinitesimal deformations and presents the proof of the well-known fact that the non-trivial infinitesimal deformations of…
Algebraically rigid simplicial complexes and graphs
Klaus Altmann, Mina Bigdeli, Juergen Herzog +1
We call a simplicial complex algebraically rigid if its Stanley-Reisner ring admits no nontrivial infinitesimal deformations, and call it inseparable if does not allow any deformat…
Simplicial complexes of whisker type
Mina Bigdeli, Jürgen Herzog, Takayuki Hibi +1
Let be a zero-dimensional monomial ideal, and be the simplicial complex whose Stanley--Reisner ideal is the polarization of . It follows from…
On the index of powers of edge ideals
Mina Bigdeli, Juergen Herzog, Rashid Zaare-Nahandi
The index of a graded ideal measures the number of linear steps in the graded minimal free resolution of the ideal. In this paper we study the index of powers and squarefree powers…