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A New Proof of Khovanskiĭ’s Theorem on the Geometry of Sumsets

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

Abstract

Khovanskiĭ studied how iterated sumsets grow geometrically, and provided the growth polynomial for sumsets as well as an approximation to lattice points inside polytopes. In this paper, we present a new proof of the theorem about geometric growth of sumsets.

Keywords

  • Sumsets
  • Geometry of numbers
  • Geometry of sumsets
  • Growth of sumsets
  • Lattice points

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  • DOI: 10.1007/978-3-319-68032-3_13
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References

  1. G.E. Bredon, Topology and Geomtry (Springer, New York, 1993)

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  2. S.S. Han, The boundary structure of the sumset in \(\mathbb{Z}^2\), in Number Theory, New York, 2003 (Springer, New York, 2004), pp. 201–218

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  3. A.G. Khovanskiĭ, The Newton polytope, the Hilbert polynomial and sums of finite sets. (Russian) Funktsional. Anal. i Prilozhen 26, 57–63, 96 (1992); translation. Funct. Anal. Appl. 26, 276–281 (1992)

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  4. J. Lee, Algebraic proof for the geometric structure of sumsets. Integers 11, 477–486 (2011)

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Correspondence to Jaewoo Lee .

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Lee, J. (2017). A New Proof of Khovanskiĭ’s Theorem on the Geometry of Sumsets. 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_13

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