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The fine triangle intersections for maximum kite packings

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Abstract

In this paper, the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let Fin(v) = {(s, t): ∃ a pair of maximum kite packings of order v intersecting in s blocks and s + t triangles}. Let Adm(v) = {(s, t): s + t ≤ b v , s, t are non-negative integers}, where b v = └v (v −1)/8┘. It is established that Fin(v) = Adm(v)\{(b v − 1, 0), (b v − 1, 1)} for any integer v ≡ 0,1 (mod 8) and v ≥ 8; Fin(v) = Adm(v) for any integer v ≡ 2, 3, 4, 5, 6,7 (mod 8) and v ≥ 4.

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Authors and Affiliations

  1. Institute of Mathematics, Beijing Jiaotong University, Beijing, 100044, P. R. China

    Gui Zhi Zhang, Yan Xun Chang & Tao Feng

  2. School of Mathematical Sciences, Hulunbuir College, Hulunbuir, 021008, P. R. China

    Gui Zhi Zhang

Authors
  1. Gui Zhi Zhang
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  2. Yan Xun Chang
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  3. Tao Feng
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Correspondence to Gui Zhi Zhang.

Additional information

Supported by the Fundamental Research Funds for the Central Universities (Grant Nos. 2011JBZ012 and 2011JBM298) and National Natural Science Foundation of China (Grant Nos. 61071221 and 10901016)

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Zhang, G.Z., Chang, Y.X. & Feng, T. The fine triangle intersections for maximum kite packings. Acta. Math. Sin.-English Ser. 29, 867–882 (2013). https://doi.org/10.1007/s10114-013-1736-9

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  • DOI: https://doi.org/10.1007/s10114-013-1736-9

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