A polynomial method for proving congruences of pω(n,m) and pν(n,m).

Recently, two partition functions p ω (n) and p ν (n) were introduced by Andrews et al. The partition function p ω (n) denotes the number of partitions of n in which each odd part is less than twice the smallest part, and p ν (n) counts the number of partitions of n into distinct non-negative parts such that all odd parts are less than twice the smallest part. Very recently, Silva et al. studied congruence properties of the restricted partition functions p ω (n , m) and p ν (n , m) which denote the number of partitions enumerated by p ω (n) and p ν (n) , respectively, into exactly m parts. In this paper, we give a polynomial method for discovering congruences for p ω (n , m) and p ν (n , m) by checking a finite number of initial values. Employing the polynomial method, we proved new and existing congruences for p ω (n , m) and p ν (n , m) based on a bounded number of calculations. For example, in order to prove that p ν (3 4 6 5 n + 1 5 6 , 5) ≡ 0 (mod 1 1) holds for all n ≥ 0 , it suffices to show that the congruence holds when 0 ≤ n ≤ 4. [ABSTRACT FROM AUTHOR]