Geodesic
Quantum continuants, quantum rotundus and triangulations of annuli
Ludivine Leclere1 ; Sophie Morier-Genoud2
1Université de Reims
2Université Reims Champagne Ardenne
The electronic journal of combinatorics, Tome 30 (2023) no. 3
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We give enumerative interpretations of the polynomials arising as numerators and denominators of the $q$-deformed rational numbers introduced by Morier-Genoud and Ovsienko. The considered polynomials are quantum analogues of the classical continuants and of their cyclically invariant versions called rotundi. The combinatorial models involve triangulations of polygons and annuli. We prove that the quantum continuants are the coarea-generating functions of paths in a triangulated polygon and that the quantum rotundi are the (co)area-generating functions of closed loops on a triangulated annulus.
DOI : 10.37236/11400
Classification : 05A15, 05A30, 11A55
Mots-clés : rotundi, quantum continuants, coarea-generating functions of paths

Ludivine Leclere  1   ; Sophie Morier-Genoud  2

1 Université de Reims
2 Université Reims Champagne Ardenne 
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     title = {Quantum continuants, quantum rotundus and triangulations of annuli},
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Ludivine Leclere; Sophie Morier-Genoud. Quantum continuants, quantum rotundus and triangulations of annuli. The electronic journal of combinatorics, Tome 30 (2023) no. 3. doi: 10.37236/11400

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