THE ADMISSIBLE MONOMIAL BASIS FOR THE POLYNOMIAL ALGEBRA OF FIVE VARIABLES IN DEGREE FOURTEEN

Let $P_k$ be the graded polynomial algebra $\mathbb{F}_2[x_1,x_2,\ldots ,x_k]$ with the degree of each generator $x_i$ being $1,$ where $\mathbb{F}_2$ denote the prime field of two elements. We study the {\it hit problem}, set up by Frank Peterson, of finding a minimal set of generators for the polynomial algebra $P_k$ as a module over the mod-2 Steenrod algebra, $\mathcal{A}$. In this paper, we explicitly determine all admissible monomials for the case $k=5$ in degree fourteen.