关于行列式展开机制的再探究

A further study on the determinant expansion mechanism

以分类求和为观点结合逆序数理论对行列式的展开机制进行探究,得到了排列标的全求和公式、逆序数降阶公式及逆序数拆分公式.利用所得公式对行列式的展开问题进行研究,给出了行列式按行展开以及Laplace展开等定理纯计算式的新证明,通过这样的研究增进了对行列式展开机制的认识.

From the point of view of classified summation and the theory of inverse ordinal number,the expansion mechanism of determinant is explored.The total sum of permutations formula,reverse ordinal number reduction formula and reverse ordinal number split formula are obtained.Using the formulas to study the expansion of determinant,a new proof of pure calculation formulas is given for theorems such as expand determinant by row and Laplace expansion.Through such a study,the understanding of determinant expansion mechanism is enhanced.