Journal of Jishou University(Natural Sciences Edition)

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Counting of One Kind of Special Permutation

TANG Baoxiang,REN Han   

  1. (1.School of Mathematics and Statistics,Tianshui Normal Institute,Tianshui 741001,Gansu China; 2.Department of Mathematics,East China Normal University,Shanghai 200062,China)
  • Online:2017-05-25 Published:2017-06-19


We have calculated the k combination f(2m,k)=f(2(m-1),k)+f(2(m-1),k-1)+f(2(m-2),k-1) of asynchronously appearing i and i+1,j and j+3,where m∈{1,2,3…},i∈{1,2,…,2m-1},j∈{1,3,5,…,2m-3},in the set S={1,2,…,2m}.Making use of inclusion and exclusion principle,we have sloved the question that they are disconnectly i element's and i+1 element's n permutation p(n)=n!+∑〖DD(〗n-1〖〗i=1〖DD)〗((-1) if (2(n-1),i)(n-i)!),where n∈{4,5,6,…},i∈{1,2,…,n-1},in the set N={1,2,3,…,n}.

Key words: strict permutation, k combination, inclusion and exclusion

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