English

Bivariate Generating Functions Enumerating Non-Bonding Dominoes on Rectangular Boards

Combinatorics 2024-04-30 v1

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.

Keywords

Cite

@article{arxiv.2404.18806,
  title  = {Bivariate Generating Functions Enumerating Non-Bonding Dominoes on Rectangular Boards},
  author = {Richard J. Mathar},
  journal= {arXiv preprint arXiv:2404.18806},
  year   = {2024}
}

Comments

15 pages, 8 figures, 13 tables, program in anc directory

R2 v1 2026-06-28T16:09:58.583Z