---
_id: '14248'
abstract:
- lang: eng
  text: "Recent work by Forsgård indicates that not every convex lattice polygon arises
    as the characteristic polygon of an affine dimer or, equivalently, an admissible
    oriented line arrangement on the torus in general position. We begin the classication
    of convex lattice polygons arising as characteristic polygons of affine dimers.
    We present several general constructions of new affine dimers from old, and an
    algorithm for finding affine dimers with prescribed polygon.\r\n\r\nWith these
    tools we prove that all lattice triangles, generalised parallelograms, and polygons
    of genus at most two admit an affine dimer."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Daniel
  full_name: Holmes, Daniel
  id: 3a443b4c-080d-11ed-979a-feb062bdcee0
  last_name: Holmes
citation:
  ama: Holmes D. Affine dimers from characteristic polygons. <i>PUMP Journal of Undergraduate
    Research</i>. 2022;5:24-51.
  apa: Holmes, D. (2022). Affine dimers from characteristic polygons. <i>PUMP Journal
    of Undergraduate Research</i>. California State University.
  chicago: Holmes, Daniel. “Affine Dimers from Characteristic Polygons.” <i>PUMP Journal
    of Undergraduate Research</i>. California State University, 2022.
  ieee: D. Holmes, “Affine dimers from characteristic polygons,” <i>PUMP Journal of
    Undergraduate Research</i>, vol. 5. California State University, pp. 24–51, 2022.
  ista: Holmes D. 2022. Affine dimers from characteristic polygons. PUMP Journal of
    Undergraduate Research. 5, 24–51.
  mla: Holmes, Daniel. “Affine Dimers from Characteristic Polygons.” <i>PUMP Journal
    of Undergraduate Research</i>, vol. 5, California State University, 2022, pp.
    24–51.
  short: D. Holmes, PUMP Journal of Undergraduate Research 5 (2022) 24–51.
corr_author: '1'
date_created: 2023-08-29T13:08:09Z
date_published: 2022-02-13T00:00:00Z
date_updated: 2024-10-09T21:06:47Z
day: '13'
extern: '1'
external_id:
  arxiv:
  - '2110.01703'
intvolume: '         5'
keyword:
- dimer model
- hyperplane arrangement
- torus
- lattice polygon
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://journals.calstate.edu/pump/article/view/2711
month: '02'
oa: 1
oa_version: Published Version
page: 24-51
publication: PUMP Journal of Undergraduate Research
publication_identifier:
  issn:
  - 2576-3725
publication_status: published
publisher: California State University
quality_controlled: '1'
status: public
title: Affine dimers from characteristic polygons
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 5
year: '2022'
...