Equidistribution and partition polynomials

Using equidistribution criteria, we establish divisibility by cyclotomic polynomials of several partition interest, including spt-crank, overpartition pairs, and t-core partitions. As corollaries, obtain new proofs various Ramanujan-type congruences for associated functions. Moreover, using results Erdös Turán, the roots on unit circle those rank, crank, spt, unimodal sequences. Our complement earlier work this topic Stanley, Boyer–Goh, others. We explain how our methods may be used to similar other offer many related open questions examples.