Seminar on Combinatorics

主講者: | 俞韋亘博士(University of Maryland) |

講題: | A note on spherical two-distance sets |

時間: | 2012-02-17 (Fri.) 15:30 - 17:00 |

地點: | 數學所 722 研討室 (台大院區) |

Abstract: | A spherical two-distance set is a ?nite collection of unit vectors in R^n such that the set of distances between any two distinct vectors has cardinality two. O.R. Musin used Delsarte’s linear programming method to prove the result when 7 ? n ? 39, except n=23. We use the semi-de?nite programming and sum of square method (SOS) to compute improved estimates of the maximum size of spherical two-distance sets. Exact answers are found for dimensions n = 23 and 40 ? n ? 94, where previous results gave divergent bounds. |

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