Corpus ID: 119673717

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

@article{Andjelic2016TheA,
  title={The \$\mu\$-permanent, a new graph labeling, and a known integer sequence},
  author={Milica Andjeli'c and C. Fonseca and Ant{\'o}nio Pereira},
  journal={arXiv: Combinatorics},
  year={2016}
}
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 $\mu$-permanent of $A$, where $\ell(\sigma)$ is the number of inversions of the permutation $\sigma$ in the symmetric group $S_n$. In this note, motivated by this notion, we discuss a new graph labeling for trees whose matrices satisfy certain $\mu$-permanental identities. We relate the number of… Expand
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