Turkish Journal of Mathematics

Abstract: Let \( \bba \) be the mod-\( p \) Steenrod Algebra. Let \( p \) be an odd prime number and \( Z_p = Z/pZ \). Let \( P_s = Z_p [x₁,x₂,\ldots,x_s]. \) A polynomial \( N \in P_s \) is said to be hit if it is in the image of the action \( A \otimes P_s \ra P_s. \) In [10] for \( p=2, \) Wood showed that if \( \a(d+s) > s \) then every polynomial of degree \( d \) in \( P_s \) is hit where \( \a(d+s) \) denotes the number of ones in the binary expansion of \( d+s \). Latter in [6] Monks extended a result of Wood to determine a new family of hit polynomials in \( P_s. \) In this paper we are interested in determining the image of the action \( A\otimes P_s \ra P_s \). So our results which determine a new family of hit polynomials in \( P_s \) for odd prime numbers generalize cononical antiautaomorphism of formulas of Davis [2], Gallant [3] and Monks [6].