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COMBINATORICS
2004
15 years 3 months ago
2004
We describe an adaptation of the billiard algorithm for finding dense packings of equal spheres inside a domain of the euclidean space. In order to improve the convergence of this...
119
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COMBINATORICS
2004
15 years 3 months ago
2004
The Ramsey game we consider in this paper is played on an unbounded set of vertices by two players, called Builder and Painter. In one move Builder introduces a new edge and Paint...
123
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COMBINATORICS
2004
15 years 3 months ago
2004
Haglund and Loehr previously conjectured two equivalent combinatorial formulas for the Hilbert series of the Garsia-Haiman diagonal harmonics modules. These formulas involve weigh...
126
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COMBINATORICS
2004
15 years 3 months ago
2004
A graph G is well-covered if every maximal independent set has the same cardinality. Let sk denote the number of independent sets of cardinality k, and define the independence pol...
114
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COMBINATORICS
2000
15 years 3 months ago
2000
We describe a new numerical procedure for generating dense packings of disks and spheres inside various geometric shapes. We believe that in some of the smaller cases, these packi...