Connectedness of graphs arising from the dual Steenrod algebra

TL;DR

This paper explores the structure and properties of graphs derived from monomials in quotients of the mod 2 dual Steenrod algebra, revealing new criteria for connectedness and insights into their combinatorial features.

Contribution

It introduces new connectedness criteria for these graphs and enhances understanding of their relation to the algebra's Hopf structure.

Findings

Established criteria for graph connectedness

Analyzed trees and Hamilton cycles in these graphs

Improved the connection between graph structure and Hopf algebra properties

Abstract

We establish connectedness criteria for graphs associated to monomials in certain quotients of the mod 2 dual Steenrod algebra. We also investigate questions about trees and Hamilton cycles in the context of these graphs. Finally, we improve upon a known connection between the graph theoretic interpretation of the mod 2 dual Steenrod algebra and its structure as a Hopf algebra.