English

Counting distinct dimer hex tilings

Combinatorics 2016-02-23 v1

Abstract

The combinatorics of tilings of a hexagon of integer side-length nn by 120 degree - 60 degree diamonds of side-length 1 has a long history, both directly (as a problem of interest in thermodynamic models) and indirectly (through the equivalence to plane partitions). Formulae as products of factorials have been conjectured and, one by one, proven for the number of such tilings under each of the symmetries of the hexagon. However, when this note was written the entry for the number of distinct such tilings in the Online Encyclopedia of Integer Sequences (OEIS) consisted of little more than a table for 0n40 \le n \le 4 and a brief discussion of those values. The aim of this note is to pull together the relevant facts.

Keywords

Cite

@article{arxiv.1602.06796,
  title  = {Counting distinct dimer hex tilings},
  author = {Peter Taylor},
  journal= {arXiv preprint arXiv:1602.06796},
  year   = {2016}
}

Comments

4 pages, 2 figures

R2 v1 2026-06-22T12:55:07.121Z