Explanipedia

Edge ideals with almost maximal finite index and their powers Open

Mina Bigdeli · 2021

Semi-Regular Sequences and Other Random Systems of Equations Open

Mina Bigdeli, Emanuela De Negri, Manuela Muzika Dizdarević, Elisa Gorla, Romy Minko , et al. · 2021

Multigraded minimal free resolutions of simplicial subclutters Open

Mina Bigdeli, Ali Akbar Yazdan Pour · 2020

Chordality, d-collapsibility, and componentwise linear ideals Open

Mina Bigdeli, Sara Faridi · 2020

Decomposable clutters and a generalization of Simon's conjectutre Open

Mina Bigdeli, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi · 2018

Each (equigenerated) squarefree monomial ideal in the polynomial ring $S=\mathbb{K}[x_1, \ldots, x_n]$ represents a family of subsets of $[n]$, called a (uniform) clutter. In this paper, we introduce a class of uniform clutters, called dec…

On the index of powers of edge ideals Open

Mina Bigdeli, Jürgen Herzog, Rashid Zaare-Nahandi · 2017

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 of edge ideals. Our results indicate that the index as a f…

Simplicial orders and chordality Open

Mina Bigdeli, Jürgen Herzog, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi · 2016

Stability of Betti numbers under reduction processes: Towards chordality of clutters Open

Mina Bigdeli, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi · 2016

Isotonian Algebras Open

Mina Bigdeli, Jürgen Herzog, Takayuki Hibi, Ayesha Asloob Qureshı, Akihiro Shikama · 2015

To a pair $P$ and $Q$ of finite posets we attach the toric ring $K[P,Q]$ whose generators are in bijection to the isotone maps from $P$ to $Q$. This class of algebras, called isotonian, are natural generalizations of the so-called Hibi rin…

Stability of Betti numbers under reduction processes: towards chordality\n of clutters Open

Mina Bigdeli, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi · 2015

For a given clutter $\\mathcal{C}$, let $I:=I ( \\bar{\\mathcal{C}} )$ be the\ncircuit ideal in the polynomial ring $S$. In this paper, we show that the Betti\nnumbers of $I$ and $I + ( \\textbf{x}_F )$ are the same in their non-linear\nst…

Toric rings, inseparability and rigidity Open

Mina Bigdeli, Jürgen Herzog, Dancheng Lu · 2015

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 a $K$-algebra $R$ are parameterized by the elements of cota…

Algebraically rigid simplicial complexes and graphs Open

Klaus Altmann, Mina Bigdeli, Juergen Herzog, Dancheng Lu · 2015

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 deformation to other simplicial complexes. Algebraically rigid simp…

Simplicial Complexes of Whisker Type Open

Mina Bigdeli, Jürgen Herzog, Takayuki Hibi, Antonio Macchia · 2015

Let $I\subset K[x_1,\ldots,x_n]$ be a zero-dimensional monomial ideal, and $\Delta(I)$ be the simplicial complex whose Stanley--Reisner ideal is the polarization of $I$. It follows from a result of Soleyman Jahan that $\Delta(I)$ is shella…

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