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On the clique number of Paley graphs of prime power order
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2021-10-01 , DOI: 10.1016/j.ffa.2021.101930 Chi Hoi Yip 1
中文翻译:
关于素数幂阶Paley图的团数
更新日期:2021-10-02
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2021-10-01 , DOI: 10.1016/j.ffa.2021.101930 Chi Hoi Yip 1
Affiliation
Finding a reasonably good upper bound for the clique number of Paley graphs is an open problem in additive combinatorics. A recent breakthrough by Hanson and Petridis using Stepanov's method gives an improved upper bound on Paley graphs defined on a prime field , where . We extend their idea to the finite field , where for a prime and a non-negative integer s. We show the clique number of the Paley graph over is at most .
中文翻译:
关于素数幂阶Paley图的团数
为 Paley 图的团数找到一个合理的上界是加法组合学中的一个悬而未决的问题。Hanson 和 Petridis 最近使用 Stepanov 方法取得的突破给出了在素域上定义的 Paley 图的改进上限, 在哪里 . 我们将他们的想法扩展到有限域, 在哪里 对于素数 和一个非负整数s。我们展示了佩雷图的团数 最多是 .