29 citations · 73 across the 8 of their papers we have counts for
19 papers
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…
The Mathieu group and its pseudogroup extension
John H. Conway, Noam D. Elkies, Jeremy L. Martin
We study a construction of the Mathieu group using a game reminiscent of Loyd's ``15-puzzle''. The elements of are realized as permutations on~12 of the~13 points…
Elliptic Curves x^3 + y^3 = k of High Rank
Noam D. Elkies, Nicholas F. Rogers
We use rational parametrizations of certain cubic surfaces and an explicit formula for descent via 3-isogeny to construct the first examples of elliptic curves E_k: x^3 + y^3 = k o…
Elliptic curves of large rank and small conductor
Noam D. Elkies, Mark Watkins
For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to ov…
Sylvester-Gallai Theorems for Complex Numbers and Quaternions
Noam Elkies, Lou M. Pretorius, Konrad J. Swanepoel
A Sylvester-Gallai (SG) configuration is a finite set S of points such that the line through any two points in S contains a third point of S. According to the Sylvester-Gallai Theo…
The conjugate dimension of algebraic numbers
Neil Berry, Arturas Dubickas, Noam D. Elkies +2
We find sharp upper and lower bounds for the degree of an algebraic number in terms of the -dimension of the space spanned by its conjugates. For all but seven nonnegative integ…