On determinants of tournaments and ${\mathcal{D}}_k$

Jing Zeng, Lihua You

Let $T$ be a tournament with $n$ vertices $v_1,\dots ,v_n$. The skew-adjacency matrix of $T$ is the $n\times n$ zero-diagonal matrix $S_T=[s_{ij}]$ in which $s_{ij}=-s_{ji}=1$ if…