Geodesic
Lattice Polygons with Two Interior Lattice Points
Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 920-933 Cet article a éte moissonné depuis la source Math-Net.Ru

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A lattice point in the plane is a point with integer coordinates. A lattice segment is a line segment whose endpoints are lattice points. A lattice polygon is a simple polygon whose vertices are lattice points. We find all convex lattice polygons in the plane up to equivalence with two interior lattice points.
Keywords: lattice point, lattice polygon, integral unimodular affine transformation. 
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     author = {Xiang Lin Wei and Ren Ding},
     title = {Lattice {Polygons} with {Two} {Interior} {Lattice} {Points}},
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Xiang Lin Wei; Ren Ding. Lattice Polygons with Two Interior Lattice Points. Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 920-933. http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a12/

[1] S. Rabinowitz, “On the number of lattice points inside a convex lattice $n$-gon”, Congr. Numer., 73 (1990), 99–124 | MR | Zbl

[2] R. Ding, K. Kołodziejczyk, G. Murphy, J. Reay, “A fast Pick-type approximation for areas of $H$-polygons”, Amer. Math. Monthly, 100:7 (1993), 669–673 | DOI | MR | Zbl

[3] K. Kołodziejczyk, “Hex-triangles with one interior $H$-point”, Ars Combin., 70 (2004), 33–45 | MR | Zbl

[4] R. Ding, J. R. Reay, J. Zhang, “Areas of generalized $H$-polygons”, J. Combin. Theory Ser. A, 77:2 (1997), 304–317 | DOI | MR | Zbl

[5] S. Rabinowitz, “A census of convex lattice polygons with at most one interior lattice point”, Ars Combin., 28 (1989), 83–96 | MR | Zbl

[6] S. Rabinowitz, “Consequences of the pentagon property”, Geombinatorics, 14 (2005), 208–220

[7] P. R. Scott, “On convex lattice polygons”, Bull. Austral. Math. Soc., 15:3 (1976), 395–399 | DOI | MR | Zbl