Bivariate Generating Functions Enumerating Non-Bonding Dominoes on Rectangular Boards
arXiv · Combinatorics(2024)
Abstract
The manuscript studies configurations of non-overlapping non-bonding dominoes
on finite rectangular boards of unit squares characterized by row and column
number. The non-bonding dominoes are defined here by the requirement that any
domino on the board shares at most one point (one of its four corner points)
with any other domino, but no edge. With the Transfer Matrix Method, rational
generating functions are derived that solve the enumeration problem entirely,
here evaluated for boards with up to six rows or columns.
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