311 citations · 1.2k across the 55 of their papers we have counts for
7 papers · 1 filter
New directions in enumerative chess problems
Noam D. Elkies
Normally a chess problem must have a unique solution, and is deemed unsound even if there are alternatives that differ only in the order in which the same moves are played. In an e…
On finite sequences satisfying linear recursions
Noam D. Elkies
For any field k and any integers m,n with 0 <= 2m <= n+1, let W_n be the k-vector space of sequences (x_0,...,x_n), and let H_m be the subset of W_n consisting of the sequences tha…
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…
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…
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 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…