Local optimality of Zaks-Perles-Wills simplices

Advances in Applied Mathematics - Tập 112 - Trang 101943 - 2020
Gennadiy Averkov1
1Fakultät 1, Brandenburgische Technische Universität Cottbus-Senftenberg, Postfach 10 13 44, 03013 Cottbus, Germany

Tài liệu tham khảo

Averkov, 2012, On the size of lattice simplices with a single interior lattice point, SIAM J. Discrete Math., 26, 515, 10.1137/110829052 Averkov, 2018, Equality case in van der Corput's inequality and collisions in multiple lattice tilings, Discrete Comput. Geom., 1 Averkov, 2011, Maximal lattice-free polyhedra: finiteness and an explicit description in dimension three, Math. Oper. Res., 36, 721, 10.1287/moor.1110.0510 Averkov, 2013, On the convergence of the affine hull of the Chvátal-Gomory closures, SIAM J. Discrete Math., 27, 1492, 10.1137/120898371 Averkov, 2015, Largest integral simplices with one interior integral point: solution of Hensley's conjecture and related results, Adv. Math., 274, 118, 10.1016/j.aim.2014.12.035 Averkov, 2017, Notions of maximality for integral lattice-free polyhedra: the case of dimension three, Math. Oper. Res., 42, 1035, 10.1287/moor.2016.0836 Averkov, 2018, Lattice simplices with a fixed positive number of interior lattice points: a nearly optimal volume bound, Int. Math. Res. Not. Balletti Balletti Barvinok, 1997, Lattice points and lattice polytopes, 133 Barvinok, 2008, Integer Points in Polyhedra, 10.4171/052 Blanco Conforti, 2015, Reverse Chvátal-Gomory rank, SIAM J. Discrete Math., 29, 166, 10.1137/140959882 Conrads, 2002, Weighted projective spaces and reflexive simplices, Manuscripta Math., 107, 215, 10.1007/s002290100235 Cox, 2011, Toric Varieties, vol. 124 Fulton, 1993, Introduction to Toric Varieties, vol. 131 Gritzmann, 1993, Lattice points, 765 Gruber, 2007, Convex and Discrete Geometry, vol. 336 Gruber, 1987, Geometry of Numbers, vol. 37 Haase, 2009, Lattice polygons and the number 2i+7, Amer. Math. Monthly, 116, 151, 10.4169/193009709X469913 Hensley, 1983, Lattice vertex polytopes with interior lattice points, Pacific J. Math., 105, 183, 10.2140/pjm.1983.105.183 Kasprzyk, 2009, Bounds on fake weighted projective space, Kodai Math. J., 32, 197, 10.2996/kmj/1245982903 Lagarias, 1991, Bounds for lattice polytopes containing a fixed number of interior points in a sublattice, Canad. J. Math., 43, 1022, 10.4153/CJM-1991-058-4 Nill, 2007, Volume and lattice points of reflexive simplices, Discrete Comput. Geom., 37, 301, 10.1007/s00454-006-1299-y Pikhurko, 2001, Lattice points in lattice polytopes, Mathematika, 48, 15, 10.1112/S0025579300014339 Scott, 1976, On convex lattice polygons, Bull. Aust. Math. Soc., 15, 395, 10.1017/S0004972700022826 Zaks, 1982, On lattice polytopes having interior lattice points, Elem. Math., 37, 44 Ziegler, 1995, Lectures on Polytopes, vol. 152