Nguyễn Sum

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math.AT2025

On the determination of the Singer transfer

Nguyen Sum

Let $P_{k}$ be the graded polynomial algebra $F_{2} [x_{1}, x_{2}, \dots, x_{k}]$ with the degree of each generator $x_{i}$ being 1, where $F_{2}$ denote the prime field of two ele…

math.AT2025

An application of the hit problem to the algebraic transfer

Nguyen Sum

Let $P_{k}$ be the polynomial algebra $F_{2} [x_{1}, x_{2}, \dots, x_{k}]$ over the field $F_{2}$ with two elements, in $k$ variables $x_{1}, x_{2}, \dots, x_{k}$ , each variable of d…

math.AT2025

A minimal set of generators for the polynomial algebra of five variables in a generic degree

Nguyen Sum, Pham Do Tai

Let $P_{k}$ be the graded polynomial algebra $F_{2} [x_{1}, x_{2}, \dots, x_{k}]$ over the prime field with two elements, $F_{2}$ , with the degree of each $x_{i}$ being 1. We study…

math.AT2024

Determination of the fifth Singer algebraic transfer in some degrees

Nguyen Sum

Let $P_{k}$ be the graded polynomial algebra $F_{2} [x_{1}, x_{2}, \dots, x_{k}]$ over the prime field $F_{2}$ with two elements and the degree of each variable $x_{i}$ being 1, an…

math.AT2024

A counter-example to Singer's conjecture for the algebraic transfer

Nguyen Sum

Write $P_{k} := F_{2} [x_{1}, x_{2}, \dots, x_{k}]$ for the polynomial algebra over the prime field $F_{2}$ with two elements, in $k$ generators $x_{1}, x_{2}, \dots, x_{k}$ , each of…