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Lattice-point generating functions for free sums of convex sets
Lattice-point generating functions free sums of convex sets Combinatorics
2012/7/11
Let $\J$ and $\K$ be convex sets in $\R^{n}$ whose affine spans intersect at a single rational point in $\J \cap \K$, and let $\J \oplus \K = \conv(\J \cup \K)$. We give expressions for the generating...
Strongly Regular Cayley Graphs, Skew Hadamard Difference Sets, and Rationality of Relative Gauss Sums
strongly regular graph skew Hadamard difference set relative Gauss sum
2012/3/1
In this paper, we give constructions of strongly regular Cayley graphs and skew Hadamard difference sets. Both constructions are based on choosing cyclotomic classes in finite fields, and our results ...
Sums of Ceiling Functions Solve Nested Recursions
Nested recursion Ceiling function Formal satisfaction Equivalence class
2011/9/15
Abstract: It is known that, for given integers s \geq 0 and j > 0, the nested recursion R(n) = R(n - s - R(n - j)) + R(n - 2j - s - R(n - 3j)) has a closed form solution for which a combinatorial inte...
The Knotting-Unknotting Game played on Sums of Rational Shadows
The Knotting-Unknotting Game Sums of Rational Shadows Combinatorics Geometric Topology
2011/9/5
Abstract: We consider the recently introduced knotting-unknotting game, in which two players take turns resolving crossings in a knot diagram which initially is missing all its crossing information. O...
Sparse Sums of Positive Semidefinite Matrices
Sparse Sums Positive Semidefinite Matrices Combinatorics
2011/9/29
Abstract: Recently there has been much interest in "sparsifying" sums of rank one matrices: modifying the coefficients such that only a few are nonzero, while approximately preserving the matrix that ...