@article{jmsa2019712,
author={Mothebe, Mbakiso Fix},
title={A Note on Admissible Monomials of Degree 2<SUP><i>¦Ë</i></SUP>?1},
journal={Journal of Mathematical Sciences and Applications},
volume={7},
number={1},
pages={10--14},
year={2019},
url={http://pubs.sciepub.com/jmsa/7/1/2},
issn={2333-8792},
abstract={Let <img src=image/abs1.png></img> be the polynomial algebra in <i>n </i>variables <i>x</i><SUB><i>i</i></SUB>, of degree one, over the field <img src=image/abs2.png></img> of two elements. The mod-2 Steenrod algebra <img src=image/abs3.png></img> acts on<b> </b><img src=image/abs4.png></img><b> </b>according to well known rules. A major problem in algebraic topology is that of determining <img src=image/abs5.png></img> the image of the action of the positively graded part of A. We are interested in the related problem of determining a basis for the quotient vector space <img src=image/abs6.png></img> Both <img src=image/abs7.png></img> and <b>Q</b>(<i>n</i>) are graded, where <b>P</b><SUP><i>d</i></SUP>(<i>n</i>) denotes the set of homogeneous polynomials of degree <i>d</i>. In this note we show that the monomial <img src=image/abs8.png></img> is the only one among all its permutation representatives that is admissible, (that is, <i>a</i><SUB><i>n </i></SUB>meets a criterion to be in a certain basis for <b>Q</b>(<i>n</i>)). We show further that if <img src=image/abs9.png></img> with <i>m </i>¡Ý <i>n, </i>then there are exactly<img src=image/abs10.png></img> permutation representatives of the product monomial<i> </i><img src=image/abs11.png></img><i> </i> that are admissible.},
doi={10.12691/jmsa-7-1-2}
publisher={Science and Education Publishing}
}