Sausages are Good Packings.
Sections of simplices.
Self-Packing of Centrally Symmetric Convex Bodies in R2 .
Self-Similar Lattice Tillings.
Semimatroids and their Tutte polynomials.
Sets with large Borsuk number.
Shape tiling.
Shelling Pseudopolyhedra.
Simple polygons with an infinite sequence of deflations.
Simulated factorizations II.
Singular points of a convex tiling.
Six little squares and how their numbers grow.
Six lonely runners.
Solid Circle-Packings in the Euclidean Plane.
Solving a ± b = 2c in elements of finite sets
We show that if A and B are finite sets of real numbers, then the number of triples (a,b,c) ∈ A × B × (A ∪ B) with a + b = 2c is at most (0.15+o(1))(|A|+|B|)² as |A| + |B| → ∞. As a corollary, if A is antisymmetric (that is, A ∩ (-A) = ∅), then there are at most (0.3+o(1))|A|² triples (a,b,c) with a,b,c ∈ A and a - b = 2c. In the general case where A is not necessarily antisymmetric, we show that the number of triples (a,b,c) with a,b,c ∈ A and a - b = 2c is at most (0.5+o(1))|A|². These estimates...
Solving the sensor cover energy problem via integer linear programming
This paper demonstrates that the sensor cover energy problem in wireless communication can be transformed into a linear programming problem with max-plus linear inequality constraints. Consequently, by a well-developed preprocessing procedure, it can be further reformulated as a 0-1 integer linear programming problem and hence tackled by the routine techniques developed in linear and integer optimization. The performance of this two-stage solution approach is evaluated on a set of randomly generated...
Some analogs of Zariski's Theorem on nodal line arrangements.
Some Basic Properties of Packing and Covering Constants.
Some Erdös-Szekeres Type Results About Point in Space.
Some problems in number theory, combinatorics and combinatorial geometry.