2 citations · 3 across the 5 of their papers we have counts for
6 papers
To count clean triangles we count on
Mizan R. Khan, Riaz R. Khan
A clean lattice triangle in is a triangle that does not contain any lattice points on its sides other than its vertices. The central goal of this paper is to count…
A Conjectural Inequality for Visible Points in Lattice Parallelograms
Gabriel Khan, Mizan R. Khan, Joydip Saha +1
Let , with and . Let denote the lattice parallelogram spanned by and , that is, $$P_{a,n} = \left\{ t_1(1,0)+ t_2(…
An Exposition of White's Characterization of Empty Lattice Tetrahedra
Mizan R. Khan, Karen M. Rogers
We give an exposition of White's characterization of empty lattice tetrahedra. In particular, we describe the second author's proof of White's theorem that appeared in her doctoral…
Two Combinatorial Geometric Problems Involving Modular Hyperbolas
Mizan R. Khan, Richard Magner, Steven Senger +1
We give a lower bound for the number of ordinary lines spanned by a modular hyperbola when the modulus is a prime power. We also give a partial answer to a question of Shparlinski.
Revisiting Toom's proof of Bulgarian Solitaire
Therese A. Hart, Gabriel Khan, Mizan R. Khan
In this article we give an exposition of Toom's proof of Bulgarian Solitaire that appeared in \emph{Kvant}. We provide more details. We also show how an application of the Chinese…
On the Convex Closure of the Graph of Modular Inversions
Mizan R. Khan, Igor E. Shparlinski, Christian L. Yankov
In this paper we give upper and lower bounds as well as a heuristic estimate on the number of vertices of the convex closure of the set $$ G_n=\left\{(a,b) : a,b\in \Z, ab \equiv 1…