Minimal width and diameter of lattice‐point‐free convex bodies

Mathematika ◽  
1981 ◽  
Vol 28 (2) ◽  
pp. 255-264 ◽  
Author(s):  
P. McMullen ◽  
J. M. Wills
Keyword(s):  
Lattice Point ◽  
Convex Bodies ◽  
Minimal Width

scholarly journals Some inequalities for planar convex sets containing one lattice point

1998 ◽  
Vol 58 (1) ◽  
pp. 159-166
Author(s):  
M. A. Hernández Cifre ◽  
S. Segura Gomis
Keyword(s):  
Lattice Point ◽  
Convex Sets ◽  
Convex Set ◽  
Integer Lattice ◽  
Minimal Width ◽  
Planar Convex

We obtain two inequalities relating the diameter and the (minimal) width with the area of a planar convex set containing exactly one point of the integer lattice in its interior. They are best possible. We then use these results to obtain some related inequalities.

Note on lattice-point-free convex bodies

1998 ◽  
Vol 126 (1) ◽  
pp. 7-12 ◽  
Author(s):  
Poh Wah Awyong ◽  
Martin Henk ◽  
Paul R. Scott
Keyword(s):  
Lattice Point ◽  
Convex Bodies

scholarly journals Lattice Point Inequalities for Centered Convex Bodies

2016 ◽  
Vol 30 (2) ◽  
pp. 1148-1158
Author(s):  
Sören Lennart Berg ◽  
Martin Henk
Keyword(s):  
Lattice Point ◽  
Convex Bodies

scholarly journals Estimates for the minimal width of polytopes inscribed in convex bodies

1989 ◽  
Vol 4 (6) ◽  
pp. 627-635 ◽  
Author(s):  
Peter Gritzmann ◽  
Marek Lassak
Keyword(s):  
Convex Bodies ◽  
Minimal Width

Covering Minima and Lattice-Point-Free Convex Bodies

1988 ◽  
Vol 128 (3) ◽  
pp. 577 ◽  
Author(s):  
Ravi Kannan ◽  
Laszlo Lovasz
Keyword(s):  
Lattice Point ◽  
Convex Bodies

scholarly journals Area-diameter and area-width relations for covering plane sets

1995 ◽  
Vol 51 (1) ◽  
pp. 163-169 ◽  
Author(s):  
Salvatore Vassallo
Keyword(s):  
Lattice Point ◽  
Convex Bodies ◽  
Plane Lattice

An area-diameter relation and an area-width relation for plane lattice-point-free-convex bodies is proved. This implies relations on covering sets with respect to general lattices.

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