S. Nguyen

activity

20142026

most citedOn the Peterson hit problem

77 citations · 320 across the 14 of their papers we have counts for

collaborators

15 papers

math.AT2026

On the hit problem of rank five

Nguyen Sum

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

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.AT2023

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.AT2023★ 32 cited

The squaring operation and the hit problem for the polynomial algebra in a type of generic degree

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 with two e…

math.AT2022★ 1 cited

The admissible monomial bases for the polynomial algebra of five variables in some types of generic degrees

Nguyen Sum

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

math.AT2021★ 5 cited

Steenrod operations on the modular invariants

Nguyen Sum

In this paper, we compute the action of the mod $p$ Steenrod operations on the modular invariants of the linear groups with $p$ an odd prime number.

math.AT2020

A note on the action of the primitive Milnor operations on the Dickson invariants

Nguyen Sum

In this note, we present a formula for the action of the primitive Milnor operations on generators of algebra of invariants of the general linear group $G L_{n} = G L (n, F_{p})$ in…

math.AT2018★ 55 cited

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

Nguyen Sum

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

math.AT2017★ 6 cited

On the action of the Steenrod algebra on the modular invariants of special linear group

Nguyen Sum

We compute the action of the Steenrod algebra on generators of algebras of invariants of special linear group $S L_{n} = S L (n, Z / p)$ in the polynomial algebra with $p$ an odd…

math.AT2017★ 1 cited

On the module structure over the Steenrod algebra of the Dickson algebra

Nguyen Sum

Let $p$ be an odd prime number. We study the problem of determining the module structure over the mod $p$ Steenrod algebra $A (p)$ of the Dickson algebra $D_{n}$ consisting o…

math.AT2017★ 49 cited

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.AT2016★ 2 cited

The squaring operartion and the Singer algebraic 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 $x_{i}$ being 1, regarded as a module over the mod-2 Steenrod algebra $\mathcal…

math.AT2015★ 55 cited

On a minimal set of generators for the polynomial algebra of five variables as a module over the Steenrod algebra

Dang Vo Phuc, Nguyen Sum

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

math.AT2014★ 37 cited

The hit problem for the polynomial algebra of four variables

Nguyen Sum

We study the problem of determining a minimal set of generators for the polynomial algebra $F_{2} [x_{1}, x_{2}, ..., x_{k}]$ as a module over the mod-2 Steenrod algebra $A$ .…

math.AT2014★ 77 cited

On the Peterson hit problem

Nguyen Sum

We study the hit problem, set up by F. Peterson, of finding a minimal set of generators for the polynomial algebra $P_{k} := F_{2} [x_{1}, x_{2}, ..., x_{k}]$ as a module over the mod-2…