Oriented posets, rank matrices and q-deformed Markov numbers

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 mode...

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Bibliographic Details
Published inDiscrete mathematics Vol. 348; no. 2; p. 114256
Main Author Kantarcı Oğuz, Ezgi
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2025
Subjects
Fence posets
Markov numbers
Rank polynomials
Fence posets
Rank polynomials
Markov numbers
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Summary: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.
ISSN:0012-365X
DOI:10.1016/j.disc.2024.114256