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arXiv · 2006.16899

The finiteness conjecture holds in SL(2,Z>=0)^2

Giovanni Panti·Davide Sclosa
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Abstract

Let A,B be matrices in SL(2,R) having trace greater than or equal to 2. Assume the pair A,B is coherently oriented, that is, can be conjugated to a pair having nonnegative entries. Assume also that either A,B^(-1) is coherently oriented as well, or A,B have integer entries. Then the Lagarias-Wang finiteness conjecture holds for the set {A,B}, with optimal product in {A,B,AB,A^2B,AB^2}. In particular, it holds for every matrix pair in SL(2,Z>=0).

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Giovanni Panti, Davide Sclosa. 2020-06-30. The finiteness conjecture holds in SL(2,Z>=0)^2. https://doi.org/10.1088/1361-6544/ac0484

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