On free p-superalgebras

In this article we consider several aspects of algebraic combinatorics and combinatorial algebra over fields of prime characteristics. P-super-Radford theorem gives the structure of the free associative algebra over a field o f prime characteristic with the new multiplication given by the super shuff le product, we show that this algebra is isomorphic to the reduced free sup er commutative algebra on s-regular words. We prove the elimination theorem for free partially commutative color Lie p-superalgebras and obtain a Schr eier type formula for free Lie p-superalgebras using formal power series te chniques.