5 citations · 21 across the 11 of their papers we have counts for
11 papers
The Yellowstone Permutation
David L. Applegate, Hans Havermann, Bob Selcoe +3
Define a sequence of positive integers by the rule that a(n) = n for 1 <= n <= 3, and for n >= 4, a(n) is the smallest number not already in the sequence which has a common factor…
The Gift Exchange Problem
David Applegate, N. J. A. Sloane
The aim of this paper is to solve the "gift exchange" problem: you are one of n players, and there are n wrapped gifts on display; when your turn comes, you can either choose any o…
Gleason's Theorem on Self-Dual Codes and Its Generalizations
N. J. A. Sloane
One of the most remarkable theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes. In the past 36 years there have been hundreds of pap…
Descending Dungeons and Iterated Base-Changing
David Applegate, Marc LeBrun, N. J. A. Sloane
For real numbers a, b> 1, let as a_b denote the result of interpreting a in base b instead of base 10. We define ``dungeons'' (as opposed to ``towers'') to be numbers of the form a…
Sloping Binary Numbers: A New Sequence Related to the Binary Numbers
David Applegate, Benoit Cloitre, Philippe Deléham +1
If the list of binary numbers is read by upward-sloping diagonals, the resulting ``sloping binary numbers'' 0, 11, 110, 101, 100, 1111, 1010, ... (or 0, 3, 6, 5, 4, 15, 10, ...) ha…
Codes and Invariant Theory
Gabriele Nebe, E. M. Rains, N. J. A. Sloane
The main theorem in this paper is a far-reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary-genus weight enumerators of self-…