311 citations · 1.2k across the 55 of their papers we have counts for
6 papers · 1 filter
Higher Nimbers in pawn endgames on large chessboards
Noam D. Elkies
We answer a question posed in [Elkies 1996] (math.CO/9905198) by constructing a class of pawn endgames on m-by-n boards that show the Nimbers *k for large k. We do this by modifyin…
Mordell-Weil lattices in characteristic 2, III: A Mordell-Weil lattice of rank 128
Noam D. Elkies
In the first paper of this series, we constructed a family of lattices in dimensions 2^{n+1} for positive integers n, and proved that the associated lattice packings of spheres equ…
Local statistics for random domino tilings of the Aztec diamond
Henry Cohn, Noam Elkies, James Propp
We prove an asymptotic formula for the probability that, if one chooses a domino tiling of a large Aztec diamond at random according to the uniform distribution on such tilings, th…
Explicit towers of Drinfeld modular curves
Noam D. Elkies
We give explicit equations for the simplest towers of Drinfeld modular curves over any finite field, and observe that they coincide with the asymptotically optimal towers of curves…
Shimura curve computations
Noam D. Elkies
We give some methods for computing equations for certain Shimura curves, natural maps between them, and special points on them. We then illustrate these methods by working out seve…
Rational points near curves and small nonzero |x^3-y^2| via lattice reduction
Noam D. Elkies
We give a new algorithm using linear approximation and lattice reduction to efficiently calculate all rational points of small height near a given plane curve C. For instance, when…