Abhishek Khetan

collaborators

3 papers

math.CO2026

A Counterexample to Nivat's Conjecture for a Non-Convex Window of Full Affine Span

Abhishek Khetan

We construct an exact cluster $F \subseteq Z^{2}$ of cardinality $8$ with full affine span, together with an $F$ -tiling $T$ , such that the orbit closure of $T$ in $\{0,1\}^{\m…

math.CO2026

A Periodicity Result for Tilings of $Z^{3}$ by Clusters of Prime-Squared Cardinality

Abhishek Khetan

We show that if $Z^{3}$ can be tiled by translated copies of a set $F \subseteq Z^{3}$ of cardinality the square of a prime then there is a weakly periodic $F$ -tiling of…

cs.DM2025

Vector Trifference

Siddharth Bhandari, Abhishek Khetan

We investigate a geometric generalization of trifference, a concept introduced by Elias in 1988 in the study of zero-error channel capacity. In the discrete setting, a code C \subs…

A Counterexample to Nivat's Conjecture for a Non-Convex Window of Full Affine Span

A Periodicity Result for Tilings of Z3 by Clusters of Prime-Squared Cardinality

Vector Trifference

A Periodicity Result for Tilings of $Z^{3}$ by Clusters of Prime-Squared Cardinality