Counting Coxeter’s friezes over a finite field via moduli spaces
Algebraic Combinatorics, Volume 4 (2021) no. 2, pp. 225-240.

We count the number of Coxeter’s friezes over a finite field. Our method uses geometric realizations of the spaces of friezes in a certain completion of the classical moduli space 0,n allowing repeated points in the configurations. Counting points in the completed moduli space over a finite field is related to the enumeration problem of counting partitions of cyclically ordered set of points into subsets containing no consecutive points. In the appendix we provide an elementary solution for this enumeration problem.

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DOI: https://doi.org/10.5802/alco.140
Classification: 13F60,  11G25,  05A18
Keywords: Frieze, Moduli space, Finite field, Partitions, Stirling numbers, cluster variety
@article{ALCO_2021__4_2_225_0,
     author = {Morier-Genoud, Sophie},
     title = {Counting Coxeter{\textquoteright}s friezes over a finite field via moduli spaces},
     journal = {Algebraic Combinatorics},
     pages = {225--240},
     publisher = {MathOA foundation},
     volume = {4},
     number = {2},
     year = {2021},
     doi = {10.5802/alco.140},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.140/}
}
Morier-Genoud, Sophie. Counting Coxeter’s friezes over a finite field via moduli spaces. Algebraic Combinatorics, Volume 4 (2021) no. 2, pp. 225-240. doi : 10.5802/alco.140. https://alco.centre-mersenne.org/articles/10.5802/alco.140/

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