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pro vyhledávání: '"Khan, Mizan R."'
The interior hull of a lattice polygon is the convex closure of the lattice points in the interior of the polygon. In this paper we give a concrete description of the interior hull of a clean lattice parallelogram. A clean parallelogram in $\mathbb{R
Externí odkaz:
http://arxiv.org/abs/2401.04356
Autor:
Khan, Mizan R., Khan, Riaz R.
A clean lattice triangle in ${\mathbb R}^2$ 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 the number of clean triangles of a given area up to unimodular equival
Externí odkaz:
http://arxiv.org/abs/2012.11081
Publikováno v:
In Earth System Governance August 2023 17
Publikováno v:
In Ecological Economics May 2023 207
Autor:
Khan, Mizan R., Rogers, Karen M.
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 thesis.
Externí odkaz:
http://arxiv.org/abs/1610.01981
Autor:
Lindamood, Danielle, Armitage, Derek *, Sharmin, Dilruba Fatima, Brouwer, Roy, Elliott, Susan J., Liu, Jennifer A., Khan, Mizan R.
Publikováno v:
In Environmental Science and Policy June 2021 120:99-107
Autor:
Khan, Mizan R.1 (AUTHOR), Khan, Riaz R.2 (AUTHOR)
Publikováno v:
Mathematical Intelligencer. Mar2023, Vol. 45 Issue 1, p9-15. 7p.
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.
Comment: 22 pages
Comment: 22 pages
Externí odkaz:
http://arxiv.org/abs/1304.6943
Publikováno v:
Annales des sciences mathematiques du Quebec 36 (2012): 477-486
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 Remainder Theorem allows us to generalize the proof.
Comment: Thi
Comment: Thi
Externí odkaz:
http://arxiv.org/abs/1101.1546