-color partition theoretic interpretations of some mock theta functions.
Let denote the number of overpartition pairs of n. Bringmann and Lovejoy (2008) proved that for n ≥ 0, . They also proved that there are infinitely many Ramanujan-type congruences modulo every power of odd primes for . Recently, Chen and Lin (2012) established some Ramanujan-type identities and explicit congruences for . Furthermore, they also constructed infinite families of congruences for modulo 3 and 5, and two congruence relations modulo 9. In this paper, we prove several new infinite...
Consider the set A={1,2,3,…,2n}, n≥3 and let x∈ A be unknown element. For given natural number S we are allowed to ask whether x belongs to a subset B of A such that the sum of the elements of B equals S. We investigate for which S it is possible to find x using a nonadaptive search.