• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.907-918
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• 2009

We extend some results involved the action of the Steenrod operations on monomials and get some corollaries on the hit problem. Then, by multiplying some special matrices, we obtain an efficient tool to compute the action of these operations.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.371-399
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• 2020

Let P_s := 𝔽₂[x₁, x₂, …, x_s] = ⊕_n⩾0(P_s)_n be the polynomial algebra viewed as a graded left module over the mod 2 Steenrod algebra, ${\mathfrak{A}}$. The grading is by the degree of the homogeneous terms (P_s)_n of degree n in the variables x₁, x₂, …, x_s of grading 1. We are interested in the hit problem, set up by F. P. Peterson, of finding a minimal system of generators for ${\mathfrak{A}}$-module P_s. Equivalently, we want to find a basis for the 𝔽₂-graded vector space ${\mathbb{F}}_2{\otimes}_{\mathfrak{A}}$ P_s. In this paper, we study the hit problem in the case s = 5 and the degree n = 5(2^t - 1) + 6 · 2^t with t an arbitrary positive integer.