Identity families of multiple harmonic sums and multiple zeta star values

Abstract

In this paper we present many new families of identities for multiple harmonic sums using binomial coefficients. Some of these generalize a few recent results of Hessami Pilehrood, Hessami Pilehrood and Tauraso [Trans. Amer. Math. Soc. 366 (2014), pp.3131–3159]. As applications we prove several conjectures involving multiple zeta star values (MZSV): the Two-one formula conjectured by Ohno and Zudilin, and a few conjectures of Imatomi et al. involving 2-3-2-1 type MZSV, where the boldfaced 2 means some finite string of 2's.