Shamil Asgarli

activity

20172026

most citedVan Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields

15 citations · 54 across the 30 of their papers we have counts for

collaborators

37 papers

math.AG2026

Covering plane curves over finite fields with lines

Shamil Asgarli, Sarthak Dassarma, Dragos Ghioca +2

We prove that, for every fixed $d \geq 2$ and $ε > 0$ , the $F_{q}$ -points of a geometrically irreducible reflexive plane curve of degree $d$ over $F_{q}$ can b…

math.AG2026

A geometric approach to the density of rank-metric codes

Shamil Asgarli, Lian Duan, Nathan Kaplan +1

We study the asymptotic density of $F_{q}$ -point-free linear sections of geometrically irreducible projective varieties over finite fields. We then apply these results to ra…

math.NT2026

Intersecting families and nonvanishing multivariate polynomials over finite fields

Shamil Asgarli, Bence Csajbók, Chi Hoi Yip

Let $P_{n, d}$ be the space of polynomials in $n$ variables over $F_{q}$ of degree at most $d$ . Two polynomials $f, g \in P_{n, d}$ intersect if $f(\mathbf a)…

math.CO2026

Defective chromatic polynomials

Shamil Asgarli, Tamsen Whitehead McGinley, Nicholas Xue

For a graph $G$ and an integer $d \geq 0$ , the defective chromatic polynomial $χ_{d} (G; k)$ counts the $k$ -colorings of $G$ in which each vertex has at most $d$ neighbors of its own co…

math.CO2026

An Erdős-Ko-Rado theorem for binary codes

Shamil Asgarli, Chi Hoi Yip

We study intersecting families of words from the Erdős-Ko-Rado perspective. When the alphabet size is $2$ , a maximum intersecting family is not necessarily a star. However, we prov…

math.CO2026

Extremal diameters of 3-coloring graphs of trees

Shamil Asgarli, Sara Krehbiel, Simon MacLean +1

Given a tree $T$ , its 3-coloring graph $C_{3} (T)$ has as vertices the proper 3-colorings of $T$ , with edges joining colorings that differ at exactly one vertex. We call the…

math.CO2025

Bell coloring graphs: realizability and reconstruction

Shamil Asgarli, Sara Krehbiel, Simon MacLean

Given a graph $G$ , the Bell $k$ -coloring graph $B_{k} (G)$ has vertices given by partitions of $V (G)$ into $k$ independent sets (allowing empty parts), with two partitions a…

math.CO2025

Improved lower bounds for the maximum order of an induced acyclic subgraph

Shamil Asgarli, Donald Falkenhagen, Kaya Hoshi

Computing the cardinality of a maximum induced acyclic vertex set in a digraph is NP-hard. Since finding an exact solution is computationally difficult, a fruitful approach is to e…

math.AG2025

Blocking sets from a union of plane curves

Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip

Motivated by a question of Erdős on blocking sets in a projective plane that intersect every line only a few times, several authors have used unions of algebraic curves to construc…

math.NT2025

Collision of orbits for families of polynomials defined over fields of positive characteristic

Shamil Asgarli, Dragos Ghioca

Let $L$ be a field of positive characteristic $p$ with a fixed algebraic closure $L$ , and let $α_{1}, α_{2}, β \in L$ . For an integer $d \geq 2$ , we consider the family of polyno…

math.CO2025

Coloring graphs as complete graph invariants

Shamil Asgarli, Sara Krehbiel, Howard W. Levinson

We investigate the extent to which the $k$ -coloring graph $C_{k} (G)$ uniquely determines the base graph $G$ and the number of colors $k$ . The vertices of $\mathcal{C}_{k}…

math.AG2025

Hypersurfaces passing through the Galois orbit of a point

Shamil Asgarli, Jonathan Love, Chi Hoi Yip

Asgarli, Ghioca, and Reichstein proved that if $K$ is a field with $∣ K ∣ > 2$ , then for any positive integers $d$ and $n$ , and separable field extension $L / K$ with degree $m=\binom{n+…

math.CO2024

Chromatic quasisymmetric functions of the path graph

Farid Aliniaeifard, Shamil Asgarli, Maria Esipova +3

We show that the chromatic quasisymmetric function (CQF) of a labeled path graph on $n$ vertices is not symmetric unless the labeling is the natural labeling $1, 2, ..., n$ or its…

math.AG2024

Linear system of geometrically irreducible plane cubics over finite fields

Shamil Asgarli, Dragos Ghioca

We examine the maximum dimension of a linear system of plane cubic curves whose $F_{q}$ -members are all geometrically irreducible. Computational evidence suggests that such…

math.AG2024

Mutual position of two smooth quadrics over finite fields

Shamil Asgarli, Chi Hoi Yip

Given two irreducible conics $C$ and $D$ over a finite field $F_{q}$ with $q$ odd, we show that there are $q^{2} /4 + O (q^{3/2})$ points $P$ in $P^{2} (F_{q})$ such…

math.CO2024

Counting subgraphs of coloring graphs

Shamil Asgarli, Sara Krehbiel, Howard W. Levinson +1

The chromatic polynomial $π_{G} (k)$ of a graph $G$ can be viewed as counting the number of vertices in a family of coloring graphs $C_{k} (G)$ associated with (proper) $k$ -co…

math.AG2023

Linear system of hypersurfaces passing through a Galois orbit

Shamil Asgarli, Dragos Ghioca, Zinovy Reichstein

Let $d$ and $n$ be positive integers, and $E / F$ be a separable field extension of degree $m = (n n + d)$ . We show that if $∣ F ∣ > 2$ , then there exists a point $P\in \mathbb{P}^n…

math.AG2023

Plane-filling curves of small degree over finite fields

Shamil Asgarli, Dragos Ghioca

A plane curve $C$ in $P^{2}$ defined over $F_{q}$ is called plane-filling if $C$ contains every $F_{q}$ -point of $P^{2}$ . Homma and Kim, building on the…

math.AG2023

Tangent-filling plane curves over finite fields

Shamil Asgarli, Dragos Ghioca

We study plane curves over finite fields whose tangent lines at smooth $F_{q}$ -points together cover all the points of $P^{2} (F_{q})$ .

math.HO2023

A Fair Shake: How close can the sum of $n$ -sided dice be to a uniform distribution?

Shamil Asgarli, Michael Hartglass, Daniel Ostrov +1

Two possibly unfair $n$ -sided dice, both labelled $1, 2, \dots, n$ , are rolled, and the sum is recorded. How should the dice's sides be weighted so that the resulting sum is close…

math.AG2023★ 5 cited

Existence of pencils with nonblocking hypersurfaces

Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip

We prove that there is a pencil of hypersurfaces in $P^{n}$ of any given degree over a finite field $F_{q}$ such that every $F_{q}$ -member of the pencil is not…

math.AG2023

Proportion of blocking curves in a pencil

Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip

Let $L$ be a pencil of plane curves defined over $F_{q}$ with no $F_{q}$ -points in its base locus. We investigate the number of curves in $L$ whos…

math.AG2022★ 2 cited

Most plane curves over finite fields are not blocking

Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip

A plane curve $C \subset P^{2}$ of degree $d$ is called \emph{blocking} if every $F_{q}$ -line in the plane meets $C$ at some $F_{q}$ -point. We prove that the pro…

math.AG2022★ 5 cited

Plane curves giving rise to blocking sets over finite fields

Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip

In recent years, many useful applications of the polynomial method have emerged in finite geometry. Indeed, algebraic curves, especially those defined by Rédei-type polynomials, ar…

Covering plane curves over finite fields with lines

A geometric approach to the density of rank-metric codes

Intersecting families and nonvanishing multivariate polynomials over finite fields

Defective chromatic polynomials

An Erdős-Ko-Rado theorem for binary codes

Extremal diameters of 3-coloring graphs of trees

Bell coloring graphs: realizability and reconstruction

Improved lower bounds for the maximum order of an induced acyclic subgraph

Blocking sets from a union of plane curves

Collision of orbits for families of polynomials defined over fields of positive characteristic

Coloring graphs as complete graph invariants

Hypersurfaces passing through the Galois orbit of a point

Chromatic quasisymmetric functions of the path graph

Linear system of geometrically irreducible plane cubics over finite fields

Mutual position of two smooth quadrics over finite fields

Counting subgraphs of coloring graphs

Linear system of hypersurfaces passing through a Galois orbit

Plane-filling curves of small degree over finite fields

Tangent-filling plane curves over finite fields

A Fair Shake: How close can the sum of n-sided dice be to a uniform distribution?

Existence of pencils with nonblocking hypersurfaces

Proportion of blocking curves in a pencil

Most plane curves over finite fields are not blocking

Plane curves giving rise to blocking sets over finite fields

A Fair Shake: How close can the sum of $n$ -sided dice be to a uniform distribution?