Data and Code for "The Nim-Sum of a Random Integer Partition"
Description
This dataset accompanies the paper "The Nim-Sum of a Random Integer Partition." It contains the exact counts of losing unordered Nim positions through total size N = 20,000. Equivalently, these are integer partitions of N whose parts have bitwise XOR equal to zero. The main data file records the OEIS index k, total size N = 2k, and the corresponding exact count, extending OEIS A048833 through index 10,000. The accompanying files include the source code for the exact Walsh-character computation, Chinese remainder reconstruction scripts, independent verification code, and the scripts used to generate the figures in the paper. The exact counts are reconstructed modulo seventeen primes and independently checked modulo an eighteenth prime not used in the reconstruction. The data and code support the computational results in Section 7 of the paper. The numerical computations are independent of the proofs of the asymptotic results.
Files
Institutions
- University of Hawaii SystemHawaii, Honolulu