Explorations into Monomer-Dimer Tilings of Planar Regions
The properties of monomer-dimer tilings of planar regions has been a focused area of study in the mathematical community for many years. Applications include areas such as diatomic molecular bonding and ice-formation. As my research has gone forth, discoveries have been made regarding the number of monomer-dimer tilings in specific regions. We also were able to characterize these larger tilings with polynomials that have not been published by others. Using mathematical programming, I have also found the probability distribution of where monomers will land in a completely random tiling of these ...
(For more, see "View full record.")