Tân Duy Nguyen

activity

20092026

most citedTriple Massey products vanish over all fields

33 citations · 53 across the 22 of their papers we have counts for

collaborators

28 papers

math.NT2026

Cyclotomic factors of rational necklace functions

Nguyen Cao Minh, Nguyen Vu Hoang Minh, Dung Nguyen +3

Necklace polynomials arise in various fields of mathematics, including combinatorics, Lie theory, and Galois theory over finite fields. Their arithmetic properties have been extens…

math.CO2026

Analytic Properties of Necklace Polynomials

Sunil K. Chebolu, Ján Mináč, Tung T. Nguyen +1

The necklace polynomials \[ M_n(x)=\frac1n\sum_{d\mid n}μ(d)x^{n/d} \] play a central role in discrete mathematics: they count aperiodic necklaces, enumerate monic irreducible poly…

math.NT2025

Supercharacters of finite abelian groups and applications to spectra of $U$ -unitary Cayley graphs

Tung T. Nguyen, Nguyen Duy Tân

We define super-Cayley graphs over a finite abelian group $G$ . Using the theory of supercharacters on $G$ , we explain how their spectra can be realized as a super-Fourier transform…

math.CO2025

Perfect state transfer on gcd-graphs over a finite Frobenius ring

Tung T. Nguyen, Nguyen Duy Tân

The existence of perfect state transfer (PST) on quantum spin networks is a fundamental problem in mathematics and physics. Various works in the literature have explored PST in gra…

math.NT2025

On gcd-graphs over finite rings

Tung T. Nguyen, Nguyen Duy Tân

Gcd-graphs represent an interesting and historically important class of integral graphs. Since the pioneering work of Klotz and Sander, numerous incarnations of these graphs have b…

math.NT2024

Isomorphic gcd-graphs over polynomial rings

Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân

Gcd-graphs over the ring of integers modulo $n$ are a simple and elegant class of integral graphs. The study of these graphs connects multiple areas of mathematics, including graph…

math.CO2024

On certain properties of the $p$ -unitary Cayley graph over a finite ring

Tung T. Nguyen, Nguyen Duy Tân

In recent work, we study certain Cayley graphs associated with a finite commutative ring and their multiplicative subgroups. Among various results that we prove, we provide the nec…

math.CO2024

On prime Cayley graphs

Maria Chudnovsky, Michal Cizek, Logan Crew +4

The decomposition of complex networks into smaller, interconnected components is a central challenge in network theory with a wide range of potential applications. In this paper, w…

math.RA2023

On the arithmetic of the join rings over finite fields

Sunil K. Chebolu, Jonathan Merzel, Ján Mináč +3

Given a collection ${G_{i}}_{i = 1}^{d}$ of finite groups and a ring $R$ , we have previously introduced and studied certain foundational properties of the join ring $\mathcal{J}_{G_1,…

math.NT2023

Fekete polynomials of principal Dirichlet characters

Shiva Chidambaram, Ján Mináč, Tung T. Nguyen +1

Fekete polynomials associated to quadratic Dirichlet characters have interesting arithmetic properties, and have been studied in many works. In this paper, we study a seemingly sim…

math.CO2022

On the Paley graph of a quadratic character

Ján Mináč, Lyle Muller, Tung T. Nguyen +1

Paley graphs form a nice link between the distribution of quadratic residues and graph theory. These graphs possess remarkable properties which make them useful in several branches…

math.RA2022

On the joins of group rings

Sunil K. Chebolu, Jonathan L. Merzel, Ján Mináč +4

Given a collection ${G_{i}}_{i = 1}^{d}$ of finite groups and a ring $R$ , we define a subring of the ring $M_{n} (R)$ ( $n = \sum_{i = 1}^{d} ∣ G_{i} ∣)$ that encompasses all the individual group…

math.NT2022★ 1 cited

On the arithmetic of generalized Fekete polynomials

Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân

For each prime number $p$ one can associate a Fekete polynomial with coefficients $- 1$ or $1$ except the constant term, which is 0. These are classical polynomials that have been s…

math.NT2022

Galois module structure of some elementary $p$ -abelian extensions

Lauren Heller, Jan Minac, Tung T. Nguyen +2

We determine the Galois module structure of the parameterizing space of elementary $p$ -abelian extensions of a field $K$ when $Gal (K / F)$ is any finite $p$ -group, under the a…

math.NT2021

Quaternion algebras and square power classes over biquadratic extensions

Frank Chemotti, Jan Minac, Tung T. Nguyen +3

Recently the Galois module structure of square power classes of a field $K$ has been computed under the action of $Gal (K / F)$ in the case where $Gal (K / F)$ is the Klein…

math.NT2021

Fekete polynomials, quadratic residues, and arithmetic

Jan Minac, Tung T. Nguyen, Nguyen Duy Tan

Fekete polynomials associate with each prime number $p$ a polynomial with coefficients $- 1$ or $1$ except the constant term, which is 0. These coefficients reflect the distribution…

math.NT2021

Further insights into the mysteries of the values of zeta functions at integers

Ján Mináč, Nguyen Duy Tân, Nguyen Tho Tung

We present a remarkably simple and surprisingly natural interpretation of the values of zeta functions at negative integers and zero. Namely we are able to relate these values to a…

math.GR2021★ 5 cited

Mild pro-p groups and the Koszulity conjectures

Jan Minac, Federico Pasini, Claudio Quadrelli +1

Let $p$ be a prime, and $F_{p}$ the field with $p$ elements. We prove that if $G$ is a mild pro- $p$ group with quadratic $F_{p}$ -cohomology algebra $H^\bullet(G,\math…

math.NT2015

Description of Galois unipotent extensions

Masoud Ataei, Jan Minac, Nguyen Duy Tan

Given an arbitrary field $F$ , we describe all Galois extensions $L / F$ whose Galois groups are isomorphic to the group of upper triangular unipotent 4-by-4 matrices with entries in…

math.NT2015

Construction of unipotent Galois extensions and Massey products

Jan Minac, Nguyen Duy Tan

For all primes $p$ and all fields, we find a sufficient and necessary condition of the existence of a unipotent Galois extension of degree $p^{6}$ . The main goal of this paper is to…

math.NT2014★ 33 cited

Triple Massey products vanish over all fields

Jan Minac, Nguyen Duy Tan

We show that the absolute Galois group of any field has the vanishing triple Massey product property. Several corollaries for the structure of maximal pro- $p$ -quotient of absolute…

math.NT2014★ 3 cited

Counting Galois $U_{4} (F_{p})$ -extensions using Massey products

Jan Minac, Nguyen Duy Tan

We use Massey products and their relations to unipotent representations to parametrize and find an explicit formula for the number of Galois extensions of a given local field with…

math.GR2014★ 2 cited

Dimensions of Zassenhaus filtration subquotients of some pro- $p$ -groups

Jan Minac, Michael Rogelstad, Nguyen Duy Tan

We compute the $F_{p}$ -dimension of an $n$ -th graded piece $G_{(n)} / G_{(n + 1)}$ of the Zassenhaus filtration for various finitely generated pro- $p$ -groups $G$ . These groups…

math.NT2014

Triple Massey products over global fields

Jan Minac, Nguyen Duy Tan

Let $K$ be a global field which contains a primitive $p$ -th root of unity, where $p$ is a prime number. M. J. Hopkins and K. G. Wickelgren showed that for $p = 2$ , any triple Massey…

Cyclotomic factors of rational necklace functions

Analytic Properties of Necklace Polynomials

Supercharacters of finite abelian groups and applications to spectra of U-unitary Cayley graphs

Perfect state transfer on gcd-graphs over a finite Frobenius ring

On gcd-graphs over finite rings

Isomorphic gcd-graphs over polynomial rings

On certain properties of the p-unitary Cayley graph over a finite ring

On prime Cayley graphs

On the arithmetic of the join rings over finite fields

Fekete polynomials of principal Dirichlet characters

On the Paley graph of a quadratic character

On the joins of group rings

On the arithmetic of generalized Fekete polynomials

Galois module structure of some elementary p-abelian extensions

Quaternion algebras and square power classes over biquadratic extensions

Fekete polynomials, quadratic residues, and arithmetic

Further insights into the mysteries of the values of zeta functions at integers

Mild pro-p groups and the Koszulity conjectures

Description of Galois unipotent extensions

Construction of unipotent Galois extensions and Massey products

Triple Massey products vanish over all fields

Counting Galois U4​(Fp​)-extensions using Massey products

Dimensions of Zassenhaus filtration subquotients of some pro-p-groups

Triple Massey products over global fields

Supercharacters of finite abelian groups and applications to spectra of $U$ -unitary Cayley graphs

On certain properties of the $p$ -unitary Cayley graph over a finite ring

Galois module structure of some elementary $p$ -abelian extensions

Counting Galois $U_{4} (F_{p})$ -extensions using Massey products

Dimensions of Zassenhaus filtration subquotients of some pro- $p$ -groups