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Beyond Beatty sequences: Complementary lattices

Part of: Combinatorics Designs and configurations

Published online by Cambridge University Press:  06 August 2020

Sam Vandervelde
Sam Vandervelde*
Affiliation:
Proof School, 973 Mission St, San Francisco, CA 94103
*
e-mail: svandervelde@proofschool.org
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Abstract

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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.

Keywords

Beatty sequencecomplementary sequencesquare lattice

MSC classification

Primary: 05A17: Partitions of integers
Secondary: 05B35: Matroids, geometric lattices

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 3 , September 2021 , pp. 499 - 511
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Copyright
© Canadian Mathematical Society 2020

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