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 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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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 = {http://www.numdam.org/articles/10.5802/alco.140/} }
TY - JOUR AU - Morier-Genoud, Sophie TI - Counting Coxeter’s friezes over a finite field via moduli spaces JO - Algebraic Combinatorics PY - 2021 SP - 225 EP - 240 VL - 4 IS - 2 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.140/ DO - 10.5802/alco.140 LA - en ID - ALCO_2021__4_2_225_0 ER -
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. http://www.numdam.org/articles/10.5802/alco.140/
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