{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T05:04:30Z","timestamp":1750309470065,"version":"3.41.0"},"reference-count":5,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2024,9,1]],"date-time":"2024-09-01T00:00:00Z","timestamp":1725148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p>\n            We resolve some open conjectures from the OEIS about Hardinian arrays (see A253217). In particular, we show via the transfer matrix method that\n            <jats:italic>\n              H\n              <jats:sub>r<\/jats:sub>\n            <\/jats:italic>\n            (\n            <jats:italic>n, k<\/jats:italic>\n            ), the number of\n            <jats:italic>n \u00d7 k<\/jats:italic>\n            Hardinian arrays with parameter\n            <jats:italic>r<\/jats:italic>\n            is a polynomial in\n            <jats:italic>n<\/jats:italic>\n            of degree\n            <jats:italic>r<\/jats:italic>\n            when\n            <jats:italic>r<\/jats:italic>\n            and\n            <jats:italic>k<\/jats:italic>\n            are fixed and\n            <jats:italic>n<\/jats:italic>\n            is sufficiently large. Our implementation of the main result in Maple and Python involves computing with large, sparse matrices, both numeric and symbolic.\n          <\/jats:p>","DOI":"10.1145\/3717582.3717589","type":"journal-article","created":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T20:41:51Z","timestamp":1739306511000},"page":"81-84","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Rectangular Hardinian Arrays"],"prefix":"10.1145","volume":"58","author":[{"given":"Robert","family":"Dougherty-Bliss","sequence":"first","affiliation":[{"name":"Department of Mathematics, Rutgers University, Piscataway, USA"}]},{"given":"George","family":"Spahn","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Rutgers University, Piscataway, USA"}]}],"member":"320","published-online":{"date-parts":[[2025,2,11]]},"reference":[{"key":"e_1_2_1_1_1","first-page":"2","article-title":"Hardinian Arrays","volume":"31","author":"Dougherty-Bliss Robert","year":"2024","unstructured":"Robert Dougherty-Bliss and Manuel Kauers. \"Hardinian Arrays\". In: El. J. Combinat. 31 (2 2024).","journal-title":"El. J. Combinat."},{"key":"e_1_2_1_2_1","volume-title":"Handbook of Combinatorics (Vol. 2). Ed. by R. L. Graham, M. Gr\u00f6tschel, and L. Lov\u00e1sz","author":"Gessel Ira","year":"1996","unstructured":"Ira Gessel and Richard Stanley. \"Algebraic Enumeration\". In: Handbook of Combinatorics (Vol. 2). Ed. by R. L. Graham, M. Gr\u00f6tschel, and L. Lov\u00e1sz. Cambridge, MA, USA: MIT Press, 1996."},{"issue":"2","key":"e_1_2_1_3_1","first-page":"3","article-title":"Some D-Finite and Some Possibly D-Finite Sequences in the OEIS","volume":"26","author":"Kauers Manuel","year":"2023","unstructured":"Manuel Kauers and Christoph Koutschan. \"Some D-Finite and Some Possibly D-Finite Sequences in the OEIS\". In: Journal of Integer Sequences 26.2 (2023), p. 3.","journal-title":"Journal of Integer Sequences"},{"key":"e_1_2_1_4_1","volume-title":"Advanced applications of the holonomic systems approach","author":"Koutschan Christoph","year":"2009","unstructured":"Christoph Koutschan. Advanced applications of the holonomic systems approach. 2009."},{"key":"e_1_2_1_5_1","volume-title":"The On-Line Encyclopedia of Integer Sequences","author":"OEIS Foundation Inc.","year":"2024","unstructured":"OEIS Foundation Inc. The On-Line Encyclopedia of Integer Sequences. 2024. url: http:\/\/oeis.org."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3717582.3717589","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3717582.3717589","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:17:15Z","timestamp":1750295835000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3717582.3717589"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["10.1145\/3717582.3717589"],"URL":"https:\/\/doi.org\/10.1145\/3717582.3717589","relation":{},"ISSN":["1932-2232","1932-2240"],"issn-type":[{"type":"print","value":"1932-2232"},{"type":"electronic","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2024,9]]},"assertion":[{"value":"2025-02-11","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}