Esther Banaian

activity

20222026

most citedA Generalization of Markov Numbers

1 citations · 1 across the 3 of their papers we have counts for

collaborators

4 papers

math.NT2026

Orderings of Generalized k-Markov Numbers

Esther Banaian, Min Huang

A $k$ -Markov number is a positive integer that appears in a positive integral solution to the Diophantine equation $x^{2} + y^{2} + z^{2} + k (x y + x z + y z) = (3 + 3 k) x y z$ . This equation wa…

math.NT2025

Orderings of k-Markov Numbers

Esther Banaian

The $k$ -Markov numbers, introduced by Gyoda and Matsushita, are those which appear in positive integral solutions to $x^{2} + y^{2} + z^{2} + k (x y + x z + y z) = (3 + 3 k) x y z$ . When $k = 0$ , t…

math.CO2025

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

Esther Banaian, Yasuaki Gyoda

Markov numbers, i.e. positive integers appearing in solutions to $x^{2} + y^{2} + z^{2} = 3 x y z$ , can be viewed as specializations of cluster variables. The second author and Matsushita g…

math.CO2022★ 1 cited

A Generalization of Markov Numbers

Esther Banaian, Archan Sen

We explore a generalization of the Markov numbers that is motivated by a specific generalized cluster algebra arising from an orbifold, in the sense of Chekhov and Shapiro. We give…