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Steinhaus' lattice point problem for polyhedra

Volume 146 / 2017

Hiroshi Maehara Colloquium Mathematicum 146 (2017), 123-128 MSC: Primary 52C07; Secondary 11P21. DOI: 10.4064/cm6213-5-2016 Published online: 23 September 2016

Abstract

It is proved that for every $d$-dimensional polyhedron $\varPi $ in ${\mathbb {R}}^d, \,d\ge 2$, with volume $n+\alpha ,\,|\alpha | \lt 1$, there is a congruent copy of $\varPi $ that contains exactly $n$ lattice points.

Authors

  • Hiroshi MaeharaRyukyu University
    Nishihara, Okinawa 903-0213, Japan
    e-mail

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