Oriented posets, rank matrices and q-deformed Markov numbers

Kantarcı Oğuz E.

Discrete Mathematics, vol.348, no.2, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 348 Issue: 2
  • Publication Date: 2025
  • Doi Number: 10.1016/j.disc.2024.114256
  • Journal Name: Discrete Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, MathSciNet, zbMATH
  • Keywords: Fence posets, Markov numbers, Rank polynomials
  • Galatasaray University Affiliated: Yes

Abstract

We define oriented posets with corresponding rank matrices, where linking two posets by an edge corresponds to matrix multiplication. In particular, linking chains via this method gives us fence posets, and taking traces gives us circular fence posets. As an application, we give a combinatorial model for q-deformed Markov numbers. We also resolve a conjecture of Leclere and Morier-Genoud and give several identities between circular rank polynomials.