十阶射影平面上椭圆不存在的证明
Nonexistence Certificates for Ovals in a Projective Plane of Order Ten
摘要：
在1983年，计算机搜索进行了椭圆在一个投影平面的秩序10。搜索是彻底和消极的，这意味着这种椭圆形不存在。然而，没有不存在的证明是由这个搜索产生的，据我们所知，搜索从来没有被独立核实。在本文中，我们将搜索椭圆在一个投影平面的10阶，并产生一个集合的不存在的证书，当考虑在一起，意味着这样的椭圆不存在。我们的搜索程序使用立方体和征服范式从满足性（SAT）检查领域，加上一个编程SAT求解器和顽皮的符号计算库从搜索中删除对称性。
英文摘要：
In 1983, a computer search was performed for ovals in a projective plane of order ten. The search was exhaustive and negative, implying that such ovals do not exist. However, no nonexistence certificates were produced by this search, and to the best of our knowledge the search has never been independently verified. In this paper, we rerun the search for ovals in a projective plane of order ten and produce a collection of nonexistence certificates that, when taken together, imply that such ovals do not exist. Our search program uses the cube-and-conquer paradigm from the field of satisfiability (SAT) checking, coupled with a programmatic SAT solver and the nauty symbolic computation library for removing symmetries from the search.
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