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Mat. Zametki, 2005, Volume 77, Issue 1, Pages 117–120 (Mi mz2474)  

This article is cited in 3 scientific papers (total in 3 papers)

A short proof of the twelve-point theorem

D. Repovša, M. B. Skopenkovb, M. Cencelja

a University of Ljubljana
b M. V. Lomonosov Moscow State University

Abstract: We present a short elementary proof of the following twelve-point theorem. Let $M$ be a convex polygon with vertices at lattice points, containing a single lattice point in its interior. Denote by $m$ (respectively, $m^*$) the number of lattice points in the boundary of $M$ (respectively, in the boundary of the dual polygon). Then $m+m^*=12$.

DOI: https://doi.org/10.4213/mzm2474

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English version:
Mathematical Notes, 2005, 77:1, 108–111

Bibliographic databases:

UDC: 514
Received: 29.06.2004

Citation: D. Repovš, M. B. Skopenkov, M. Cencelj, “A short proof of the twelve-point theorem”, Mat. Zametki, 77:1 (2005), 117–120; Math. Notes, 77:1 (2005), 108–111

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Victor Batyrev, Dorothee Juny, “Classification of Gorenstein toric Del Pezzo varieties in arbitrary dimension”, Mosc. Math. J., 10:2 (2010), 285–316  mathnet  crossref  mathscinet
    2. Zivaljevic R.T., “Rotation Number of a Unimodular Cycle: an Elementary Approach”, Discrete Math., 313:20 (2013), 2253–2261  crossref  mathscinet  zmath  isi  scopus
    3. Higashitani A., Masuda M., “Lattice Multipolygons”, Kyoto J. Math., 57:4 (2017), 807–828  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
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