SOME CONGRUENCES FOR PARTITIONS THAT ARE P-CORES

Authors
GARVAN FG
Citation
Fg. Garvan, SOME CONGRUENCES FOR PARTITIONS THAT ARE P-CORES, Proceedings of the London Mathematical Society, 66, 1993, pp. 449-478
Citations number
23
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the London Mathematical Society → ACNP
ISSN journal
00246115
Volume
66
Year of publication
1993
Part
3
Pages
449 - 478
Database
ISI
SICI code
0024-6115(1993)66:<449:SCFPTA>2.0.ZU;2-M
Abstract
A number of linear congruences modulo r are proved for the number of p artitions that are p-cores where p is prime, 5 less-than-or-equal-to p less-than-or-equal-to 23, and r is any prime divisor of 1/2(p - 1). A nalogous results are derived for the number of irreducible p-modular r epresentations of the symmetric group S(n). The congruences are proved using the theory of modular forms.