Skew Pieri Rules for Hall-Littlewood Functions

We produce skew Pieri Rules for Hall–Littlewood functions in the spirit of Assaf and McNamara. The first two were conjectured by the first author. The key ingredients in the proofs are a q-binomial identity for skew partitions and a Hopf algebraic identity that expands products of skew elements in terms of the coproduct and the antipode.