Journal of Mathematical Sciences and Applications
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Journal of Mathematical Sciences and Applications. 2019, 7(1), 10-14
DOI: 10.12691/jmsa-7-1-2
Open AccessArticle

A Note on Admissible Monomials of Degree 2λ−1

Mbakiso Fix Mothebe1,

1Department of Mathematics, University of Botswana, Pvt Bag 00704, Gaborone, Botswana

Pub. Date: December 30, 2019

Cite this paper:
Mbakiso Fix Mothebe. A Note on Admissible Monomials of Degree 2λ−1. Journal of Mathematical Sciences and Applications. 2019; 7(1):10-14. doi: 10.12691/jmsa-7-1-2

Abstract

Let be the polynomial algebra in n variables xi, of degree one, over the field of two elements. The mod-2 Steenrod algebra acts on according to well known rules. A major problem in algebraic topology is that of determining 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 Both and Q(n) are graded, where Pd(n) denotes the set of homogeneous polynomials of degree d. In this note we show that the monomial is the only one among all its permutation representatives that is admissible, (that is, an meets a criterion to be in a certain basis for Q(n)). We show further that if with m n, then there are exactly permutation representatives of the product monomial that are admissible.

Keywords:
Steenrod squares polynomial algebra Peterson hit problem

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References:

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