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Beyond Beatty sequences: Complementary lattices
Published online by Cambridge University Press: 06 August 2020
Abstract
By taking square lattices as a two-dimensional analogue to Beatty sequences, we are motivated to define and explore the notion of complementary lattices. In particular, we present a continuous one-parameter family of complementary lattices. This main result then yields several novel examples of complementary sequences, along with a geometric proof of the fundamental property of Beatty sequences.
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- © Canadian Mathematical Society 2020