Trimer covers in the triangular grid: twenty mostly open problems
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929213149282304 |
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| author | Propp, James |
| author_facet | Propp, James |
| contents | In the past three decades, the study of rhombus tilings and domino tilings of various plane regions has been a thriving subfield of enumerative combinatorics. Physicists classify such work as the study of dimer covers of finite graphs. In this article we move beyond dimer covers to trimer covers, introducing plane regions called benzels that play a role analogous to hexagons for rhombus tilings and Aztec diamonds for domino tilings, inasmuch as one finds many (so far mostly conjectural) exact formulas governing the number of tilings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_06472 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Trimer covers in the triangular grid: twenty mostly open problems Propp, James Combinatorics 52C20, 05B50 In the past three decades, the study of rhombus tilings and domino tilings of various plane regions has been a thriving subfield of enumerative combinatorics. Physicists classify such work as the study of dimer covers of finite graphs. In this article we move beyond dimer covers to trimer covers, introducing plane regions called benzels that play a role analogous to hexagons for rhombus tilings and Aztec diamonds for domino tilings, inasmuch as one finds many (so far mostly conjectural) exact formulas governing the number of tilings. |
| title | Trimer covers in the triangular grid: twenty mostly open problems |
| topic | Combinatorics 52C20, 05B50 |
| url | https://arxiv.org/abs/2206.06472 |