The $\mu$-permanent, a new graph labeling, and a known integer sequence

Milica Anđelić, Carlos M. da Fonseca, António Pereira

Let $A=(a_{ij})$ be an $n$-by-$n$ matrix. For any real number $\mu$, we define the polynomial $$P_{\mu }(A)=\sum _{\sigma \in S_n}{a}_{1\sigma (1)}\cdots a_{n\sigma (n)}{\mu }^{\ell (\sigma )},$$ as the $\mu$-permane…