160722(4)

Ruby

A2n−1 型からBn 型への折り畳み

上下が対称なA2n−1 型の (Conway-Coxeter) フリーズパターンを作成するこ とによって、

Bn 型のフリーズパターンを構成できることを確かめてみた。

def A(ary)
  m = ary.size
  a_ary = [ary]
  p a_ary[0]
  i = 0
  while i == 0 || a_ary[i] != ary
    a_ary << Array.new(m, 1)
    (m - 2).downto(1){|j| a_ary[i + 1][j] = (a_ary[i][j - 1] * a_ary[i + 1][j + 1] + 1) / a_ary[i][j]}
    p a_ary[i + 1]
    i += 1
  end
end

def B(ary)
  m = ary.size 
  a_ary = [ary]
  p a_ary[0]
  i = 0
  while i == 0 || a_ary[i] != ary
    a_ary << Array.new(m, 1)
    (m - 2).downto(1){|j| a_ary[i + 1][j] = (a_ary[i][j - 1] * a_ary[i + 1][j + 1] + 1) / a_ary[i][j]}
    a_ary[i + 1][0] = (a_ary[i + 1][1] * a_ary[i + 1][1] + 1) / a_ary[i][0]
    p a_ary[i + 1]
    i += 1
  end
end

A([1, 2, 7, 12, 29, 17, 5, 3, 1])
p ''
B([29, 17, 5, 3, 1])

出力結果
[1, 2, 7, 12, 29, 17, 5, 3, 1]
[1, 1, 1, 3, 5, 12, 7, 2, 1]
[1, 3, 2, 1, 2, 3, 7, 4, 1]
[1, 2, 5, 3, 1, 1, 1, 2, 1]
[1, 4, 7, 17, 10, 3, 2, 1, 1]
[1, 2, 7, 12, 29, 17, 5, 3, 1]
""
[29, 17, 5, 3, 1]
[5, 12, 7, 2, 1]
[2, 3, 7, 4, 1]
[1, 1, 1, 2, 1]
[10, 3, 2, 1, 1]
[29, 17, 5, 3, 1]