Abstract
For given positive integers p and q, let f(p,q) be the smallest integer n such that {0,1,...,3n – 1} can be partitioned into congruent copies of a 3-point set {0,p, p + q}. It is shown that f(p,q) is approximately at most 5q/3 for any fixed p and large q. Moreover, g(p) := lim sup q→ ∞ f(p,q)/q is studied. It is proved that g(2k) = 4/3 or 5/3 and g(2k + 1) = 1 for k ≥ 1.
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© 2000 Springer-Verlag Berlin Heidelberg
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Nakamigawa, T. (2000). One-Dimensional Tilings with Congruent Copies of a 3-Point Set. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 1998. Lecture Notes in Computer Science, vol 1763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46515-7_19
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DOI: https://doi.org/10.1007/978-3-540-46515-7_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67181-7
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