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Drunken X-mas polynomials for graphs
Given a finite connected graph $\Gamma$ with vertices $\lbrace 1,\ldots,N\rbrace$,
we can consider the polynomial
$$\sum_{\pi\in\mathcal S_N}x^{\sum_{j=1}^Nd_\Gamma(j,\pi(j))}$$
where $\mathcal S_N$ ...
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