{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T15:40:02Z","timestamp":1742226002644,"version":"3.38.0"},"reference-count":9,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T00:00:00Z","timestamp":1717459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T00:00:00Z","timestamp":1717459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2025,4]]},"abstract":"Abstract<\/jats:title>\n We introduce the multi-width of a lattice polytope and use this to classify and count all lattice tetrahedra with multi-width \n \n $$(1,w_2,w_3)$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n 1<\/mml:mn>\n ,<\/mml:mo>\n \n w<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \n w<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msub>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>. The approach used in this classification can be extended into a computer algorithm to classify lattice tetrahedra of any given multi-width. We use this to classify tetrahedra with multi-width \n \n $$(2,w_2,w_3)$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n 2<\/mml:mn>\n ,<\/mml:mo>\n \n w<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \n w<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msub>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> for small \n \n $$w_2$$<\/jats:tex-math>\n \n \n w<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> and \n \n $$w_3$$<\/jats:tex-math>\n \n \n w<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> and make conjectures about the function counting lattice tetrahedra of any multi-width.<\/jats:p>","DOI":"10.1007\/s00454-024-00659-5","type":"journal-article","created":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T20:16:45Z","timestamp":1717532205000},"page":"859-885","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Classification of Width 1 Lattice Tetrahedra by Their Multi-Width"],"prefix":"10.1007","volume":"73","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-2097-3294","authenticated-orcid":false,"given":"Girtrude","family":"Hamm","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,4]]},"reference":[{"key":"659_CR1","doi-asserted-by":"publisher","first-page":"3871","DOI":"10.1093\/imrn\/rny130","volume":"13","author":"G Averkov","year":"2020","unstructured":"Averkov, G., Kr\u00fcmpelmann, J., Nill, B.: Lattice simplices with a fixed positive number of interior lattice points: a nearly optimal volume bound. Int. Math. Res. Not. IMRN 13, 3871\u20133885 (2020). https:\/\/doi.org\/10.1093\/imrn\/rny130","journal-title":"Int. Math. Res. Not. IMRN"},{"issue":"4","key":"659_CR2","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1287\/moor.1110.0510","volume":"36","author":"G Averkov","year":"2011","unstructured":"Averkov, G., Wagner, C., Weismantel, R.: Maximal lattice-free polyhedra: finiteness and an explicit description in dimension three. Math. Oper. Res. 36(4), 721\u2013742 (2011). https:\/\/doi.org\/10.1287\/moor.1110.0510","journal-title":"Math. Oper. Res."},{"key":"659_CR3","unstructured":"Hamm, G.: Classification of lattice triangles by their two smallest widths. arXiv Preprint (2023). arXiv:2304.03007"},{"key":"659_CR4","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.7802562","author":"G Hamm","year":"2023","unstructured":"Hamm, G.: Width 2 tetrahedra with small multi-width. 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