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White’s Theorem

An Exposition of White’s Characterization of Empty Lattice Tetrahedra

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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 220)

Abstract

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 (Rogers in Doctoral dissertation 1993) [7].

Keywords

  • Lattice tetrahedron
  • Empty lattice polyhedron

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  • DOI: 10.1007/978-3-319-68032-3_11
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Acknowledgements

This article is a variant of an earlier manuscript drafted and submitted in the early 1990s. It was written in collaboration with Therese Hart who did the initial calculations that led us to discover White’s result. We withdrew the article after discovering that White had anticipated our main discovery three decades previously. We would like to express our gratitude to Mel Nathanson who encouraged us to write this expository piece.

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Correspondence to Mizan R. Khan .

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Khan, M.R., Rogers, K.M. (2017). White’s Theorem. In: Nathanson, M. (eds) Combinatorial and Additive Number Theory II. CANT CANT 2015 2016. Springer Proceedings in Mathematics & Statistics, vol 220. Springer, Cham. https://doi.org/10.1007/978-3-319-68032-3_11

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