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Modulating flow polynomials and parity bias in homological walk counting
Long weighted walks seem to sample mod-$t$ flows uniformly, but at even moduli a persistent parity bias survives. Writing $C_G(t)$ for the flow polynomial of a connected graph $G$ of genus $g$, the proportion of nowhere-zero flows under uniform sampling is $C_G(t)/t^g$. For arbitrary positive direct
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