TY - UNPB
T1 - Comptage des quiddités sur les corps finis et sur quelques anneaux ℤ/Nℤ
AU - Cuntz, Michael
AU - Mabilat, Flavien
PY - 2023/4/6
Y1 - 2023/4/6
N2 - The λ-quiddities of size n are n-tuples of elements of a fixed set, solutions of a matrix equation appearing in the study of Coxeter friezes. These can be considered on various sets with very different structures from one set to another. The main objective of this text is to obtain explicit formulas giving the number of λ-quiddities of size n over finite fields and over the rings ℤ/Nℤ with N=4m and m square free. We will also give some elements about the asymptotic behavior of the number of λ-quiddities verifying an irreducibility condition over ℤ/Nℤ when N goes to the infinity.
AB - The λ-quiddities of size n are n-tuples of elements of a fixed set, solutions of a matrix equation appearing in the study of Coxeter friezes. These can be considered on various sets with very different structures from one set to another. The main objective of this text is to obtain explicit formulas giving the number of λ-quiddities of size n over finite fields and over the rings ℤ/Nℤ with N=4m and m square free. We will also give some elements about the asymptotic behavior of the number of λ-quiddities verifying an irreducibility condition over ℤ/Nℤ when N goes to the infinity.
U2 - 10.48550/arXiv.2304.03071
DO - 10.48550/arXiv.2304.03071
M3 - Preprint
BT - Comptage des quiddités sur les corps finis et sur quelques anneaux ℤ/Nℤ
ER -