Oriented posets, rank matrices and q-deformed Markov numbers

Kantarcı Oğuz E.

Discrete Mathematics, cilt.348, sa.2, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 348 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1016/j.disc.2024.114256
  • Dergi Adı: Discrete Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, MathSciNet, zbMATH
  • Anahtar Kelimeler: Fence posets, Markov numbers, Rank polynomials
  • Galatasaray Üniversitesi Adresli: Evet

Özet

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.