Yes, that sounds right. Thanks for the correction!

]]>Yes, sorry, that was a mild abuse of notation. You need the data of the sources and sinks.

]]>“Immediately” was a bit of an overstatement. The argument I had in mind is that the multiplicativity of the determinant is a polynomial identity in variables and that Lindstrom-Gessel-Viennot supplies enough cases of this identity to prove it, although this isn’t obvious and ought to require some work.

]]>No, it doesn’t. You would have to know that (almost) all determinants can be realized as nonpermutable path configurations.

]]>Interesting, but not entirely surprising. In my opinion this is a fundamental property of the determinant.

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