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.
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References
G.E. Bredon, Topology and Geomtry (Springer, New York, 1993)
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
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)
J. Lee, Algebraic proof for the geometric structure of sumsets. Integers 11, 477–486 (2011)
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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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DOI: https://doi.org/10.1007/978-3-319-68032-3_13
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