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Dukes, Peter J.; Gaede, Tao

Families of modular arithmetic progressions with an interval of distance multiplicities. (English) Zbl 1514.05027

Integers 23, Paper A25, 17 p. (2023).

MSC:

05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors
11B25 Arithmetic progressions
52C10 Erdős problems and related topics of discrete geometry

Keywords:

Euclidean distance problem of Erdős; Erdős-deep pairs
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Full Text: arXiv Link

References:

[1] P. Arnoux, Sturmian sequences, in Substitutions in Dynamics, Arithmetics and Combina-torics, 143-198, Lecture Notes in Math. 1794, Springer, Berlin, 2002.
[2] E. Brown, The fabulous (11, 5, 2) biplane, Math. Mag. 77 (2004), 87-100. · Zbl 1176.05011
[3] D. Burt, E. Goldstein, S. Manski, S.J. Miller, E.A. Palsson, H. Suh, Crescent configurations, Integers 16 (2016), #A38. · Zbl 1354.52018
[4] E.D. Demaine, F. Gomez-Martin, H. Meijer, D. Rappaport, P. Taslakian, G.T. Toussaint, T. Winograd and D.R. Wood, The distance geometry of music, Comput. Geom. 42 (2009), 429-454.
[5] P. Erdős, On sets of distances of n points, Amer. Math. Monthly 53 (1946), 248-250. · Zbl 0060.34805
[6] P. Erdős, Problem E2938, Amer. Math. Monthly 89 (1982), no 4., 273.
[7] P. Erdős, Distances with specified multiplicities, Amer. Math. Monthly 96 (1989), no. 5, 447.
[8] T. Gaede, Erdős-deep families of arithmetic progressions, M.Sc. thesis, University of Victoria, 2022.
[9] J. Garibaldi, A. Iosevich and S. Senger, The Erdős Distance Problem, Student Mathematical Library 56, American Mathematical Society, Providence, RI, 2011. · Zbl 1234.00002
[10] L. Guth and N.H. Katz, On the Erdős distinct distances problem in the plane, Ann. of Math. (2) 181 (2015), 155-190. · Zbl 1310.52019
[11] A. Iosevich and M. Rudnev, Erdős distance problem in vector spaces over finite fields, Trans. Amer. Math. Soc. 359 (2007), 6127-6142. · Zbl 1145.11083
[12] I. Palásti, A distance problem of P. Erdős with some further restrictions, Discrete Math. 76 (1989), 155-156. · Zbl 0669.52007
[13] G.T. Toussaint, The Geometry of Musical Rhythm, CRC Press, Boca Raton, FL, 2013. · Zbl 1275.00024
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