%0 Journal Article %T Modular coinvariants and the mod p homology of QS^k %A Phan H. Chon %J Mathematics %D 2014 %I arXiv %X We use modular invariant theory to establish a complete set of relations of the mod $p$ homology of $\{QS^k\}_{k\geq0}$, for $p$ odd, as a ring object in the category of coalgebras (also known as a coalgebraic ring or a Hopf ring). We also describe the action of the mod $p$ Dyer-Lashof algebra as well as the mod $p$ Steenrod algebra on the coalgebraic ring. %U http://arxiv.org/abs/1412.7588v2