Turkish Journal of MathematicsOn the Action of Steenrod Operations on Polynomial Algebras
Bethlehem, PA 18015-USA
Abstract: Let \( \bba \) be the mod-\( p \) Steenrod Algebra. Let \( p \) be an odd prime number and \( Zp = Z/pZ \). Let \( Ps = Zp [x1,x2,\ldots,xs]. \) A polynomial \( N \in Ps \) is said to be hit if it is in the image of the action \( A \otimes Ps \ra Ps. \) In  for \( p=2, \) Wood showed that if \( \a(d+s) > s \) then every polynomial of degree \( d \) in \( Ps \) is hit where \( \a(d+s) \) denotes the number of ones in the binary expansion of \( d+s \). Latter in  Monks extended a result of Wood to determine a new family of hit polynomials in \( Ps. \) In this paper we are interested in determining the image of the action \( A\otimes Ps \ra Ps \). So our results which determine a new family of hit polynomials in \( Ps \) for odd prime numbers generalize cononical antiautaomorphism of formulas of Davis , Gallant  and Monks .
Turk. J. Math., 22, (1998), 163-170.
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Other articles published in the same issue: Turk. J. Math.,vol.22,iss.2.