10 papers
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 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…
Supercharacters of finite abelian groups and applications to spectra of -unitary Cayley graphs
Tung T. Nguyen, Nguyen Duy Tân
We define super-Cayley graphs over a finite abelian group . Using the theory of supercharacters on , we explain how their spectra can be realized as a super-Fourier transform…
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…
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…
Isomorphic gcd-graphs over polynomial rings
Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân
Gcd-graphs over the ring of integers modulo are a simple and elegant class of integral graphs. The study of these graphs connects multiple areas of mathematics, including graph…