TITLE: Change of basis, monomial relations, and $P_t^s$ bases for the
       Steenrod algebra

AUTHOR: Ken Monks
        Department of Mathematics
        University of Scranton
        Scranton, PA 18510
        email: monks@uofs.edu

FILENAME: BASES.DVI

ABSTRACT:

The relationship between several common bases for the mod 2 Steenrod algebra
is explored and a family of bases consisting of monomials in distinct
$P_t^s$'s is developed. A recursive change of basis formula is produced to
convert between the Milnor basis and each of the bases for which the change
of basis matrix in every grading is upper triangular. In particular, it is
shown that the basis of admissible monomials, the $P_t^s$ bases, and two
bases due to D. Arnon, are all bases having this property, and the
corresponding change of basis formula is produced for each of them. Some
monomial relations for the mod 2 Steenrod algebra are then obtained by
exploring the change of basis transformations.