Flavien Mabilat - Combinatorial description of the principal congruence subgroup Γ(2) in SL(2, Z)

cm:9039 - Communications in Mathematics, March 30, 2022, Volume 30 (2022), Issue 1 - https://doi.org/10.46298/cm.9039
Combinatorial description of the principal congruence subgroup Γ(2) in SL(2, Z)

Authors: Flavien Mabilat

We characterize sequences of positive integers (c 1 , c 2 , ..., cn) for which the (2 × 2)-matrix c 1 −1 1 0 · · · cn −1 1 0 belongs to the principal congruence subgroup of level 2 in SL(2, Z). The answer is given in terms of dissections of a convex n-gon into a mixture of triangles and quadrilaterals.


Volume: Volume 30 (2022), Issue 1
Published on: March 30, 2022
Accepted on: February 3, 2022
Submitted on: February 3, 2022
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]


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