Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903679 | Journal of Combinatorial Theory, Series A | 2019 | 30 Pages |
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 (n2) 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Tri Lai,