Premium
Some Congruences for Partitions that are p ‐Cores
Author(s) -
Garvan Frank G.
Publication year - 1993
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-66.3.449
Subject(s) - congruence relation , mathematics , prime (order theory) , modulo , divisor (algebraic geometry) , modular form , combinatorics , pure mathematics , arithmetic
A number of linear congruences modulo r are proved for the number of partitions that are p ‐cores where p is prime, 5 ⩽ p ⩽ 23, and r is any prime divisor of ½( p − 1). Analogous results are derived for the number of irreducible p ‐modular representations of the symmetric group S n . The congruences are proved using the theory of modular forms.