29 citations · 129 across the 12 of their papers we have counts for
5 papers · 1 filter
Lattices and codes with long shadows
Noam D. Elkies
In an earlier paper (math.NT/9906019) we showed that any integral unimodular lattice L of rank n which is not isometric with Z^n has a characteristic vector of norm at most n-8. [A…
A characterization of the Z^n lattice
Noam D. Elkies
We use theta series and modular forms to prove that Z^n is the only integral unimodular lattice of rank n without characteristic vectors of norm <n, i.e. the only integral unimodul…
On numbers and endgames: Combinatorial game theory in chess endgames
Noam D. Elkies
In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Gu…
The identification of three moduli spaces
Noam D. Elkies
It is one of the wonderful ``coincidences'' of the theory of finite groups that the simple group G of order 25920 arises as both a symplectic group in characteristic 3 and a unitar…
The still-Life density problem and its generalizations
Noam D. Elkies
A "still Life" is a subset S of the square lattice Z^2 fixed under the transition rule of Conway's Game of Life, i.e. a subset satisfying the following three conditions: 1. No elem…