Eigenvalues and Eigenvectors of the Matrix of Permutation Counts

Pawan Auorora, Shashank K Mehta

Define a $(n^4+n^2)/2\times (n^4+n^2)/2$ symmetric $B$. $(ij)(kl)$ is an index where $i,j,k,l\in [n]$, $(ab)$ is an unordered pair and $(kl)$ is an ordered pair when $i\ne j$, oth…