We establish connectedness criteria for graphs associated to monomials in certain quotients of the mod 2 dual Steenrod algebra \(\mathscr {A}^*\). 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 \(\mathscr {A}^*\) and its structure as a Hopf algebra.

中文翻译：

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由对偶 Steenrod 代数产生的图的连通性

我们为与 mod 2 对偶 Steenrod 代数\(\mathscr {A}^*\)的某些商中的单项式相关的图建立连通性标准。我们还在这些图表的背景下研究有关树和汉密尔顿循环的问题。最后，我们改进了\(\mathscr {A}^*\)的图论解释与其作为 Hopf 代数的结构之间的已知联系。