H. Saremi

activity

20152025

most citedVertex decomposability and weakly polymatroidal ideals

1 citations · 1 across the 4 of their papers we have counts for

collaborators

8 papers

math.AC2025

Sequentially Cohen-Macaulay and pretty clean monomial ideals

Amir Mafi, Rando Rasul Qadir, Hero Saremi

Let $R = K [x_{1}, \dots, x_{n}]$ be the polynomial ring in $n$ variables over a field $K$ and $I$ be monomial ideal of $R$ . In this paper, we show that if $I$ is a generic monomial ideal…

math.AC2024

Unmixed polymatroidal ideals

Mozghan Koolani, Amir Mafi, Hero Saremi

Let $R = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ and $I$ be a polymatroidal ideal of $R$ . In this paper, we provide a comprehensive classifica…

math.AC2022

Strong persistence and associated prime of powers of monomial ideals

Amir Mafi, Hero Saremi

Let $R = K [x_{1}, \dots, x_{n}]$ be the polynomial ring in $n$ variables over a field $K$ and $I$ be a monomial ideal of degree $d \leq 2$ . We show that $(I^{k + 1} : I) = I^{k}$ for all $k\geq 1…

math.AC2022★ 1 cited

Vertex decomposability and weakly polymatroidal ideals

Amir Mafi, Dler Naderi, Hero Saremi

Let $K$ be a field and $R = K [x_{1}, \dots, x_{n}]$ be the polynomial ring in $n$ variables over a field $K$ . Let $Δ$ be a simplicial complex on $n$ vertices and $I = I_{Δ}$ be its Stanley-R…

math.AC2019

Unmixedness and arithmetic properties of matroidal ideals

Hero Saremi, Amir Mafi

Let $R = k [x_{1}, ..., x_{n}]$ be the polynomial ring in $n$ variables over a field $k$ and $I$ be a matroidal ideal of degree $d$ . In this paper, we study the unmixedness properties and t…

math.AC2019

Sequentially Cohen-Macaulay matroidal ideals

Madineh Jafari, Amir Mafi, Hero Saremi

Let $R = K [x_{1}, ..., x_{n}]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a matroidal ideal of degree $d$ in $R$ . In this paper, we study the class of sequenti…

math.AC2016

Hilbert Regularity of Stanley-Reisner Rings

Winfried Bruns, Hero Saremi

In this note, we characterize the Hilbert regularity of the Stanley-Reisner ring $K [△]$ in terms of the $f$ -vector and the $h$ -vector of a simplicial complex $\bigtria…

math.AC2015

Relative Hilbert co-efficients

Amir Mafi, Tony J. Puthenpurakal, Rakesh B. T. Reddy +1

Let $(A,\m)$ be a \CM \ local ring of dimension $d$ and let $I \subseteq J$ be two $\m$-primary ideals with $I$ a reduction of $J$ . For $i = 0, \dots, d$ let $e_{i}^{J} (A)$ ( $e_{i}^{I} (A)$ )…