Abstract
We generalize the construction of Gabber and Galil to essentially every unimodular matrix in SL 2(Z). It is shown that every parabolic or hyperbolic fractional linear transformation explicitly defines an expander of bounded degree and constant expansion. Thus all but a vanishingly small fraction of unimodular matrices define expanders.
Research supported in part by NSF grant CCR-9820806 and by a Guggenheim Fellowship.
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Cai, JY. (2000). Essentially Every Unimodular Matrix Defines an Expander. In: Goos, G., Hartmanis, J., van Leeuwen, J., Lee, D.T., Teng, SH. (eds) Algorithms and Computation. ISAAC 2000. Lecture Notes in Computer Science, vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40996-3_2
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DOI: https://doi.org/10.1007/3-540-40996-3_2
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