Boris Shapiro

Transposition Cayley Spectra and Subgraph Counts

Let $G$ be a finite simple graph on the vertex set $[n]$, and let $\Gamma(G)$ be the Cayley graph of the symmetric group $S_n$ generated by the transpositions corresponding to the edges of $G$. We study the inverse spectral problem for the assignment $G\mapsto \Gamma(G)$ through the group-algebra operator $A_G=\sum_{\{...