A New Infinite Family of Hemisystems of the Hermitian Surface

Abstract

In this paper, we construct an infinite family of hemisystems of the Hermitian surface H(3, q2). In particular, we show that for every odd prime power q congruent to 3 modulo 4, there exists a hemisystem of H(3, q2) admitting \(C_{\left( {q^3 + 1} \right)/4} :C_3 \).

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Correspondence to Qing Xiang.

Additional information

The first author acknowledges the support of the Australian Research Council Future Fellowship FT120100036.

The second author acknowledges the support of a Hackett Postgraduate Research Scholarship.

The third author acknowledges the support by JSPS under Grant-in-Aid for Young Scientists (B) 25800093 and Scientific Research (B) 15H03636.

The fourth author acknowledges the support of an NSF grant DMS-1600850.

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Bamberg, J., Lee, M., Momihara, K. et al. A New Infinite Family of Hemisystems of the Hermitian Surface. Combinatorica 38, 43–66 (2018). https://doi.org/10.1007/s00493-016-3525-4

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Mathematics Subject Classification (2000)

  • 05B25
  • 05E30
  • 51E12