{"abstract":[{"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.","lang":"eng"}],"external_id":{"arxiv":["2110.01703"]},"type":"journal_article","extern":"1","date_created":"2023-08-29T13:08:09Z","publication":"PUMP Journal of Undergraduate Research","main_file_link":[{"open_access":"1","url":"https://journals.calstate.edu/pump/article/view/2711"}],"publication_identifier":{"issn":["2576-3725"]},"month":"02","page":"24-51","date_updated":"2023-09-05T09:28:32Z","intvolume":"         5","title":"Affine dimers from characteristic polygons","article_type":"original","language":[{"iso":"eng"}],"publication_status":"published","keyword":["dimer model","hyperplane arrangement","torus","lattice polygon"],"year":"2022","citation":{"chicago":"Holmes, Daniel. “Affine Dimers from Characteristic Polygons.” <i>PUMP Journal of Undergraduate Research</i>. California State University, 2022.","short":"D. Holmes, PUMP Journal of Undergraduate Research 5 (2022) 24–51.","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.","ama":"Holmes D. Affine dimers from characteristic polygons. <i>PUMP Journal of Undergraduate Research</i>. 2022;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.","apa":"Holmes, D. (2022). Affine dimers from characteristic polygons. <i>PUMP Journal of Undergraduate Research</i>. California State University."},"date_published":"2022-02-13T00:00:00Z","status":"public","publisher":"California State University","oa":1,"oa_version":"Published Version","volume":5,"author":[{"first_name":"Daniel","id":"3a443b4c-080d-11ed-979a-feb062bdcee0","last_name":"Holmes","full_name":"Holmes, Daniel"}],"quality_controlled":"1","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"14248","day":"13"}