All Questions

Define $\mathcal M_n$ as the set of all $n\times n$ matrices with each entry either 1 or $x$. Two such matrices are equivalent iff they can be obtained from each other by swapping pairs of rows and ...

(a) Let $[n] = \{1,\dotsc,n\}$, and let $\pi:[n]\to [n]$ be a permutation. Define an $n$-by-$n$ matrix $A=A(\pi)$ as follows: $A_{i,j}=1$ if $j>i$ and $\pi(j)>\pi(i)$, $A_{i,j}=-1$ If $j<i$ ...

$\DeclareMathOperator\ora{ora}$Let $A_0$ be the adjacency matrix of graph $G$ and $P_0$ permutation matrix of multiplicative order $\rho$. Let $X$ be positive integer and $B_0=P_0^X A_0 P_0^{-X}$. Q1 ...