Monthly Archives: February 2013

Ann Lehman’s Sculpture Based on Herb Scarf’s Maximal Lattice Free Convex Bodies

Posted on February 22, 2013 by Gil Kalai

Maximal lattice-free convex bodies introduced by Herb Scarf and the related complex of maximal lattice free simplices (also known as the Scarf complex) are remarkable geometric constructions with deep connections to combinatorics, convex geometry, integer programming, game theory, fixed point computations, … Continue reading →

Posted in Art, Computer Science and Optimization, Economics, Games | Tagged , | 5 Comments

F ≤ 4E

Posted on February 1, 2013 by Gil Kalai

1. E ≤ 3V Let G be a simple planar graph with V vertices and E edges. It follows from Euler’s theorem that E ≤ 3V In fact, we have (when V is at least 3,) that E ≤ 3V – 6. … Continue reading →

Posted in Combinatorics, Convex polytopes, Geometry, Open problems | Tagged | 14 Comments