Author

Phúc Võ Dang

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Preprint Jul 2026

Two-Sided Dimension Bounds for the Peterson Hit Problem via Projections and Matrix Minors

Let $\mathcal P_k=\mathbb F_2[x_1,\ldots,x_k]$ be the polynomial algebra over the prime field $\mathbb F_2$, viewed as an unstable module over the mod-$2$ Steenrod algebra $\mathcal A$. The well-known Peterson hit problem asks for a minimal set of generators for the $\mathcal A$-module $\mathcal P_k$. This is equivalen...

Phúc Võ Dang, Peter V. Danchev · 0 citations

Preprint Sep 2026

Binary Minor Certificates for the $\mathcal A(1)$-hit problem of $MO(2)$

Let $M=\widetilde H^*(MO(2);\mathbb F_2)$ and let $\mathcal A(1)$ be the subalgebra of the mod $2$ Steenrod algebra generated by $\operatorname{Sq}^1$ and $\operatorname{Sq}^2$. In this work, we determine the quotient $\mathbb F_2\otimes_{\mathcal A(1)}M$ in every internal degree $h\geq0$, where internal degree $h$ cor...

Phúc Võ Dang · 0 citations

Preprint Jul 2026

The rank-five Peterson hit problem, the fifth Singer transfer, and a geometric generator in unoriented cobordism

The Peterson hit problem seeks a minimal set of generators for the polynomial algebra $P_s = \mathbb{F}_2[x_1,\dots,x_s]$ as an unstable module over the mod-2 Steenrod algebra $\mathcal{A}$. For rank five, general admissible bases fail, and the interplay between Kameko periodicity and modular invariants becomes computa...

Phúc Võ Dang · 0 citations