Multiplication and combinatorics in the Steenrod algebra Original Research Article

This paper is concerned with multiplication in the mod-2 Steenrod algebra, as expressed in terms of both the Milnor basis and the basis of admissible elements. Part I describes techniques for graphically representing Milnor basis elements and for interpreting combinatorially the matrices that arise in their multiplication table, and Part II provides a method for the simultaneous computation of families of Adem relations. Part III combines the techniques of Parts I and II to identify constraints on the Milnor basis elements which occur in the image under the canonical anti-automorphism of certain products.