Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
419978 | Discrete Applied Mathematics | 2011 | 4 Pages |
Abstract
Let spt(n) denote Andrews’ smallest part statistic. Andrews discovered congruences for spt(n) mod 5,75,7 and 13 which are reminiscent of Ramanujan’s classical partition congruences for moduli 5, 7, and 11. We create an algorithm exploiting a recursive pattern in Andrews’ smallest part statistic, spt(n), to generate modular residues of spt values in quadratic time and linear working memory. We use this algorithm to acquire the first million values of spt(n). On the basis of the data, we make conjectures about the existence of hundreds of thousands of new congruences including a simple modulus 11 congruence that was found and proved independently by Garvan.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
K.C. Garrett, C. McEachern, T. Frederick, O. Hall-Holt,