论文标题
计数多重复合数字
Counting Involutions on Multicomplex Numbers
论文作者
论文摘要
我们表明，多符号数量$ n $的实线自动形态和签名的$ 2^{n-1} $之间的实际自动形态之间存在培训。这使我们能够推断出多重复合数字的许多结果，包括用于多重复合空间上的次数数量的公式，该公式将最新结果推广到双色杂志数字上，并与季节案例形成鲜明对比。我们还将此公式推广到$ r $ involutions，并获得保留基本假想单元的互动数量的公式。这些证明依赖于与多符合数字有关的新基本结果，这些结果在文献中出人意料地未知，包括计数和代表定理，以平方为$ \ pm 1 $。
We show that there is a bijection between real-linear automorphisms of the multicomplex numbers of order $n$ and signed permutations of length $2^{n-1}$. This allows us to deduce a number of results on the multicomplex numbers, including a formula for the number of involutions on multicomplex spaces which generalizes a recent result on the bicomplex numbers and contrasts drastically with the quaternion case. We also generalize this formula to $r$-involutions and obtain a formula for the number of involutions preserving elementary imaginary units. The proofs rely on new elementary results pertaining to multicomplex numbers that are surprisingly unknown in the literature, including a count and a representation theorem for numbers squaring to $\pm 1$.
