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

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Showing 2026Show all

6 papers · 1 filter

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…