Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $\mu$-permanent, a new graph labeling, and a known integer sequence   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 labelings of a path with a known integer
sequence. Several examples are provided.

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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys