TAOCP 5.1.4: Tableaux and Involutions
Section 5.1.4 exercises: 12/12 solved.
Section 5.1.4. Tableaux and Involutions
Exercises from TAOCP Volume 3 Section 5.1.4: 12/12 solved.
| # | Rating | Category | Status | Time |
|---|---|---|---|---|
| 1 | [**] | verified | 43m18s | |
| 2 | [**] | verified | 14m53s | |
| 3 | [**] | verified | 1m26s | |
| 4 | [**] | verified | 2m42s | |
| 5 | [**] | solved | 3m41s | |
| 6 | [20] | medium | verified | 1m17s |
| 7 | [M24] | math-medium | solved | 42m04s |
| 8 | [M28] | math-hard | verified | 56m28s |
| 9 | [M43] | math-project | solved | 11m30s |
| 10 | [M20] | math-medium | solved | 16m42s |
| 11 | [M08] | math-simple | solved | 46m42s |
| 12 | [HM25] | hm-medium | solved | 10m59s |
TAOCP 5.1.4 Exercise 1
Let \begin{pmatrix} a_1&a_2&\cdots&a_9\\ b_1&b_2&\cdots&b_9 \end{pmatrix}
TAOCP 5.1.4 Exercise 2
For each entry $a_i$ of the permutation, let $t_i$ be the class defined in the text.
TAOCP 5.1.4 Exercise 3
Let $P$ be the tableau corresponding to a permutation $a_1 a_2 \dots a_m$.
TAOCP 5.1.4 Exercise 4
Let a permutation $\pi = a_1 a_2 \cdots a_{n^2}$ of $\{1,2,\dots,n^2\}$.
TAOCP 5.1.4 Exercise 5
We give a complete corrected proof by isolating the precise mechanism that guarantees both row and column inequalities during each bumping operation, without circular reasoning.
TAOCP 5.1.4 Exercise 6
Let Algorithm S be the full sequence of insertions described in Algorithm I applied successively, terminating with a tableau $P$ and a final added position $(r,s)$ determined at the last insertion ste...
TAOCP 5.1.4 Exercise 7
Let $P$ be a tableau of shape $(m_1,m_2,\dots,m_k)$, with $m_1 \ge m_2 \ge \dots \ge m_k > 0$.
TAOCP 5.1.4 Exercise 8
**Exercise 5.
TAOCP 5.1.4 Exercise 9
Let M= \begin{pmatrix} q_1&q_2&\cdots&q_n\\ p_1&p_2&\cdots&p_n
TAOCP 5.1.4 Exercise 10
Let N(a,b,c) denote the number of permutations of the multiset