11 papers
Sums of units in finite rings and applications to Cayley graphs
Ján MináÄ, Tung T. Nguyen, Nguyen Duy Tân
The question of whether a ring is additively generated by its units has been studied from several perspectives in ring theory and algebraic graph theory. In this paper, we investig…
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…
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…
Analytic Properties of Necklace Polynomials
Sunil K. Chebolu, Ján MináÄ, 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 pol…
On -unitary Cayley graphs over finite rings
Tung T. Nguyen, Nguyen Duy Tân
Graphs defined over a finite ring are well-studied in the literature. Due to their nature, these types of graphs connect several branches of mathematics, including algebra, number…
Maximal -extensions of Pythagorean fields and Right Angled Artin Groups
Oussama Hamza, Christian Maire, Ján MinÃ¡Ä +1
In this paper, we describe minimal presentations of maximal pro- quotients of absolute Galois groups of formally real Pythagorean fields of finite type. For this purpose, we int…