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arXiv · 1507.02611

Proof of a conjecture of Kenyon and Wilson on semicontiguous minors

Tri Lai
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Abstract

Kenyon and Wilson showed how to test if a circular planar electrical network with $n$ nodes is well-connected by checking the positivity of $\binom{n}{2}$ central minors of the response matrix. Their test is based on the fact that any contiguous minor of a matrix can be expressed as a Laurent polynomial in the central minors. Moreover, the Laurent polynomial is the generating function of domino tilings of a weighted Aztec diamond. They conjectured that a larger family of minors, semicontiguous minors, can also be written in terms of domino tilings of a region on the square lattice. In this paper, we present a proof of the conjecture.

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Tri Lai. 2015-07-09. Proof of a conjecture of Kenyon and Wilson on semicontiguous minors. https://arxiv.org/abs/1507.02611

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