English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let $P_n$ be the graded polynomial algebra $\mathbb F_2[x_1,x_2,\ldots ,x_n]$with the degree of each generator $x_i$ being 1, where $\mathbb F_2$ denote theprime field of two elements.  The Peterson hit problem is to find a minimal generating set for $P_n$regarded as a module over the mod-2 Steenrod algebra, $\mathcal{A}$.Equivalently, we want to find a vector space basis for $\mathbb F_2\otimes_{\mathcal A} P_n$ in each degree $d$. Such a basis may be representedby a list of monomials of degree $d$.  In this paper, we present a construction for the $\mathcal A$-generators of$P_n$ and prove some properties of it. We also explicitly determine a basis of$\mathbb F_2 \otimes_{\mathcal A} P_n$ for $n = 5$ and the degree $d = 15.2^s -5$ with $s$ an arbitrary positive integer. These results are used to verifySinger's conjecture for the fifth Singer algebraic transfer in respectivedegree.

On a construction for the generators of the polynomial algebra as a module over the Steenrod algebra