Geodesic
Beyond Beatty sequences: Complementary lattices
Canadian mathematical bulletin, Tome 64 (2021) no. 3, pp. 499-511

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DOI

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.
DOI : 10.4153/S0008439520000594
Mots-clés : Beatty sequence, complementary sequence, square lattice 
Vandervelde, Sam. Beyond Beatty sequences: Complementary lattices. Canadian mathematical bulletin, Tome 64 (2021) no. 3, pp. 499-511. doi: 10.4153/S0008439520000594
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     title = {Beyond {Beatty} sequences: {Complementary} lattices},
     journal = {Canadian mathematical bulletin},
     pages = {499--511},
     year = {2021},
     volume = {64},
     number = {3},
     doi = {10.4153/S0008439520000594},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000594/}
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