2015/07/09 by Lai, Tri
#05A15 #05B45 #05C50 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1507.02611
Kenyon and Wilson showed how to test if a circular planar electrical network with n nodes is well-connected by checking the positivity of \binomn2 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.