求下列各排列的逆序数.(1) 341782659;(2) 987654321;(3) n(n-1)…321;(4) 13…(2n-1)(2n)(2n-2)…2.
举一反三
- 排列\(13...(2n-1)(2n)(2n-2)...42\)的逆序数为 A: \(n(n+1)\) B: \(n(n+1)/2\) C: \(n(n-1)/2\) D: \(n(n-1)\)
- 排列\( n(n - 1)(n - 2) \cdots 3 \cdot 2 \cdot 1 \)的逆序数是( ) A: \( {1 \over 2}n(n - 1) \) B: \( n(n - 1) \) C: \( n \) D: \( {n^2}(n - 1) \)
- 设`\n`阶方阵`\A`满足`\|A| = 2`,则`\|A^TA| = ,|A^{ - 1}| = ,| A^ ** | = ,| (A^ ** )^ ** | = ,|(A^ ** )^{ - 1} + A| = ,| A^{ - 1}(A^ ** + A^{ - 1})A| = `分别等于( ) A: \[4,\frac{1}{2},{2^{n - 1}},{2^{{{(n - 1)}^2}}},2{(\frac{3}{2})^n},\frac{{{3^n}}}{2}\] B: \[2,\frac{1}{2},{2^{n - 1}},{2^{{{(n + 1)}^2}}},2{(\frac{3}{2})^n},\frac{{{3^n}}}{2}\] C: \[4,\frac{1}{2},{2^{n + 1}},{2^{{{(n - 1)}^2}}},2{(\frac{3}{2})^{n - 1}},\frac{{{3^n}}}{2}\] D: \[2,\frac{1}{2},{2^{n - 1}},{2^{{{(n - 1)}^2}}},2{(\frac{3}{2})^{n - 1}},\frac{{{3^n}}}{2}\]
- 求下列各排列的逆序数: (1)341782659 ; (2)987654321; (3) ; (4).08bf9085832a9039c6a2676821065e69.pnged1a6eb6ca55093b15e0f6d710c8f72b.png
- 设自然数从小到大为标准次序,则排列13...(2n-1)24...(2n)的逆序数为 A: n(n-1) B: n(n-1)/2 C: n(n+1) D: n(n+1)/2