Research on the Combinatorial Transform Mathematics Problem Frog Leap

Tian Zeng High school affiliated to Renmin university of China

S.-T. Yau High School Science Awarded Papers mathscidoc:1608.35028

2009
In this paper we extend and deepen a shortlist for the 37th International Mathematical Olympiad (IMO) and propose the Frog Leap Commute Theorem and the Queue Polynomial. We explore the problem from the following aspects: (1) Make use of semi-invariants and propose the Frog Leap Commute Theorem. (2) Make extensions regarding frogs leaping to opposite directions on a straight line. (3) Research frogs leaping to the same direction on a straight line and solve the minimum number of frogs satisfying an infinite leap. (4) Extend the problem to leaps on a plane or in space. (5) Research and extend problems regarding frogs leaping on a circle. (6) Estimate the function c(n) and calculate the order of the function.
Frog Leap Leap Commute Theorem Queue Polynomial Positive State
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@inproceedings{tian2009research,
  title={Research on the Combinatorial Transform Mathematics Problem Frog Leap},
  author={Tian Zeng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160813215155232148076},
  year={2009},
}
Tian Zeng. Research on the Combinatorial Transform Mathematics Problem Frog Leap. 2009. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160813215155232148076.
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