Square - Partition Congruences
نویسنده
چکیده
منابع مشابه
Parity Results for Certain Partition Functions
Blecksmith, Brillhart and Gerst proved four congruences modulo 2 involving partition generating functions of the following sort. 1 . Y n∈S (1 − q) ≡ 1 + X n≥1 q 2 + X n≥1 q 2 (mod 2) where S = {n > 0 : n ≡ ±(1, 2, 3, 4) or 6 (mod 12)}. We give simple and uniform proofs of their congruences and of several others of the same sort. Each of these congruences yields a theorem on partitions. Thus the...
متن کاملCongruences for Andrews’ Spt-function
Congruences are found modulo powers of 5, 7 and 13 for Andrews’ smallest parts partition function spt(n). These congruences are reminiscent of Ramanujan’s partition congruences modulo powers of 5, 7 and 11. Recently, Ono proved explicit Ramanujan-type congruences for spt(n) modulo ` for all primes ` ≥ 5 which were conjectured earlier by the author. We extend Ono’s method to handle the powers of...
متن کاملCongruences for Andrews ’ Spt - Function modulo Powers of 5 , 7 and 13
Abstract. Congruences are found modulo powers of 5, 7 and 13 for Andrews’ smallest parts partition function spt(n). These congruences are reminiscent of Ramanujan’s partition congruences modulo powers of 5, 7 and 11. Recently, Ono proved explicit Ramanujan-type congruences for spt(n) modulo for all primes ≥ 5 which were conjectured earlier by the author. We extend Ono’s method to handle the pow...
متن کاملGeneralized Congruence Properties of the Restricted Partition Function P (n,m)
Ramanujan-type congruences for the unrestricted partition function p(n) are well known and have been studied in great detail. The existence of Ramanujan-type congruences are virtually unknown for p(n,m), the closely related restricted partition function that enumerates the number of partitions of n into exactly m parts. Let ` be any odd prime. In this paper we establish explicit Ramanujan-type ...
متن کاملNon-existence of Ramanujan Congruences in Modular Forms of Level Four
Abstract. Ramanujan famously found congruences for the partition function like p(5n + 4) ≡ 0 (mod 5). We provide a method to find all simple congruences of this type in the coefficients of the inverse of a modular form on Γ1(4) which is non-vanishing on the upper half plane. This is applied to answer open questions about the (non)-existence of congruences in the generating functions for overpar...
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