Anubhab Ghosal

collaborators

6 papers

math.CO2026

The extensible no-four-on-a-circle problem

Anubhab Ghosal, Ritesh Goenka

We show that there exists a set $S \subset Z^{2}$ containing no four points on a circle or a line such that $∣ S \cap [n]^{2} ∣ = Ω (n)$ as $n \to \infty$ . Since any no-f…

math.CO2026

On the largest size of sum-free sets in symmetric regions

Anubhab Ghosal, Dmitry Tsarev

A subset $S$ of a group $G$ is said to be sum-free (resp. $Δ$ -free) if there are no solutions to $a + b = c$ (resp. $a + b + c = 0$ ) with $a, b, c \in S$ . For a convex region $R\subset\mathbb{R…

math.CO2026

No- $(k + 1)$ -in-line problem for $k ⩾ 3$

Anubhab Ghosal, Ritesh Goenka, Alexandr Grebennikov +3

What is the maximum number of points one can place in an $n \times n$ grid such that every Euclidean line contains at most $k$ points? For $k = 2$ , this is the notorious no-three-i…

math.CO2026

A note on the extensible no-three-in-line problem

Anubhab Ghosal

We show the existence of a set $S \subset Z^{2}$ avoiding collinear triples satisfying $∣ S \cap [n]^{2} ∣ = Ω (n / lo g n)$ for sufficiently large $n$ . This improves on the best…

math.CO2025

On the number of sum-free subsets of the square grid

Anubhab Ghosal

Generalising the Cameron--Erdős conjecture to two dimensions, Elsholtz and Rackham conjectured that the number of sum-free subsets of $[n]^{2}$ is $2^{0.6 n^{2} + O (n)}$ . We prove their c…

math.CO2025

On subsets of lattice cubes avoiding affine and spherical degeneracies

Anubhab Ghosal, Ritesh Goenka, Peter Keevash

For integers $1 < k < d - 1$ and $r \geq k + 2$ , we establish new lower bounds on the maximum number of points in $[n]^{d}$ such that no $r$ lie in a $k$ -dimensional affine (or linear) su…

The extensible no-four-on-a-circle problem

On the largest size of sum-free sets in symmetric regions

No-(k+1)-in-line problem for k⩾3

A note on the extensible no-three-in-line problem

On the number of sum-free subsets of the square grid

On subsets of lattice cubes avoiding affine and spherical degeneracies

No- $(k + 1)$ -in-line problem for $k ⩾ 3$