4 citations · 6 across the 3 of their papers we have counts for
5 papers
Trees, forests, and total positivity: I. -trees and -forests matrices
Tomack Gilmore
We consider matrices with entries that are polynomials in arising from natural -generalisations of two well-known formulas that count: forests on vertices with compo…
Coefficientwise total positivity of some matrices defined by linear recurrences
Xi Chen, Bishal Deb, Alexander Dyachenko +2
We exhibit a lower-triangular matrix of polynomials in six indeterminates that appears empirically to be coefficientwise totally positive, and which includes as a…
Inverting the Kasteleyn matrix for holey hexagons
Tomack Gilmore
Consider a semi-regular hexagon on the triangular lattice (that is, the lattice consisting of unit equilateral triangles, drawn so that one family of lines is vertical). Rhombus (o…
Interactions between interleaving holes in a sea of unit rhombi
Tomack Gilmore
Consider a family of collinear, equilateral triangular holes of any even side length lying within a sea of unit rhombi. The results presented below show that as the distance betwee…
Three interactions of holes in two dimensional dimer systems
Tomack Gilmore
Consider the unit triangular lattice in the plane with origin , drawn so that one of the sets of lattice lines is vertical. Let and denote respectively the vertical and…