Mathematica,字母代

Question

如果我有一个字母表,让我们说sigma = {1,2,3,4,a,b,c,d,e,f,g}并想生成长度为n的所有单词,有没有办法做到这一点？

我可以Flatten[Outer[Function[{x, y}, {x, y}], sigma, sigma], 1]为wordlength = 2做到这一点,但它并没有更多的字母.排列不起作用,因为它不包括双打. Permutations[sigma, {2}] 例如,不给{a,a}.

有没有一种简单的方法可以做到这一点,或者我必须为它编写一个函数？

这对于n = 2是正确的(但我想要任意n):

{{1, 1}, {1, 2}, {1, 3}, {1, 4}, {1, a}, {1, b}, {1, c}, {1, d}, {1, 
  e}, {1, f}, {1, g}, {2, 1}, {2, 2}, {2, 3}, {2, 4}, {2, a}, {2, 
  b}, {2, c}, {2, d}, {2, e}, {2, f}, {2, g}, {3, 1}, {3, 2}, {3, 
  3}, {3, 4}, {3, a}, {3, b}, {3, c}, {3, d}, {3, e}, {3, f}, {3, 
  g}, {4, 1}, {4, 2}, {4, 3}, {4, 4}, {4, a}, {4, b}, {4, c}, {4, 
  d}, {4, e}, {4, f}, {4, g}, {a, 1}, {a, 2}, {a, 3}, {a, 4}, {a, 
  a}, {a, b}, {a, c}, {a, d}, {a, e}, {a, f}, {a, g}, {b, 1}, {b, 
  2}, {b, 3}, {b, 4}, {b, a}, {b, b}, {b, c}, {b, d}, {b, e}, {b, 
  f}, {b, g}, {c, 1}, {c, 2}, {c, 3}, {c, 4}, {c, a}, {c, b}, {c, 
  c}, {c, d}, {c, e}, {c, f}, {c, g}, {d, 1}, {d, 2}, {d, 3}, {d, 
  4}, {d, a}, {d, b}, {d, c}, {d, d}, {d, e}, {d, f}, {d, g}, {e, 
  1}, {e, 2}, {e, 3}, {e, 4}, {e, a}, {e, b}, {e, c}, {e, d}, {e, 
  e}, {e, f}, {e, g}, {f, 1}, {f, 2}, {f, 3}, {f, 4}, {f, a}, {f, 
  b}, {f, c}, {f, d}, {f, e}, {f, f}, {f, g}, {g, 1}, {g, 2}, {g, 
  3}, {g, 4}, {g, a}, {g, b}, {g, c}, {g, d}, {g, e}, {g, f}, {g, g}}

Answer 1

Tuples[sigma, n]

Answer 2

虽然Tuples肯定是更好的方法,但我认为向您展示使现有方法适用于任意n值的方法很有价值.

Flatten[Outer[List, ##], n - 1] & @@ ConstantArray[sigma, n]

这可以通过创建n实例sigma和排序(##)来实现Outer. Flatten用于删除除最后一级括号之外的所有括号.

观察您Function[{x, y}, {x, y}]可以简单地替换List.

您也可以使用此Distribute功能,假设您的字母表本身不包含列表.

Distribute[ConstantArray[sigma, n], List]