{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T13:35:48Z","timestamp":1781530548522,"version":"3.54.1"},"reference-count":25,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T00:00:00Z","timestamp":1702944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we consider the sum of divisors d of n such that n\/d is a power of 2 and derive a new decomposition for the number of plane partitions of n in terms of binomial coefficients as a sum over partitions of n. In this context, we introduce a new combinatorial interpretation of the number of plane partitions of n.<\/jats:p>","DOI":"10.3390\/sym16010005","type":"journal-article","created":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T11:17:24Z","timestamp":1702984644000},"page":"5","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Plane Partitions and Divisors"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3221-6864","authenticated-orcid":false,"given":"Cristina","family":"Ballantine","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, College of The Holy Cross, Worcester, MA 01610, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8411-2928","authenticated-orcid":false,"given":"Mircea","family":"Merca","sequence":"additional","affiliation":[{"name":"Department of Mathematical Methods and Models, Fundamental Sciences Applied in Engineering Research Center, National University of Science and Technology Politehnica Bucharest, Bucharest 060042, Romania"},{"name":"Academy of Romanian Scientists, Bucharest 050044, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,19]]},"reference":[{"key":"ref_1","unstructured":"Andrews, G.E. (1998). The Theory of Partitions, Cambridge Mathematical Library, Cambridge University Press. Reprint of the 1976 original."},{"key":"ref_2","first-page":"619","article-title":"Memoir on the theory of the partition of numbers, I","volume":"187","author":"MacMahon","year":"1897","journal-title":"Lond. Phil. Trans. A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/0097-3165(87)90045-8","article-title":"Rogers-Rarnanujam identities for partitions with \u201cN copies of N\u201d","volume":"45","author":"Agarwal","year":"1987","journal-title":"J. Combin. Theory Ser. A"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Bressoud, D.M. (1999). Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture, Cambridge University Press.","DOI":"10.1017\/CBO9780511613449"},{"key":"ref_5","unstructured":"Sloane, N.J.A. (2023, November 22). The On-Line Enciclopedia of Integer Sequences. Available online: http:\/\/oeis.org."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Merca, M., and Radu, I.-I. (2023). Plane partitions as sums over partitions. Symmetry, 15.","DOI":"10.3390\/sym15101820"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"47","DOI":"10.2307\/3608532","article-title":"The Josephus problem","volume":"44","author":"Robinson","year":"1960","journal-title":"Math. Gaz."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1016\/j.jcta.2012.05.001","article-title":"The truncated pentagonal number theorem","volume":"119","author":"Andrews","year":"2012","journal-title":"J. Combin. Theory Ser. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.jcta.2018.06.011","article-title":"Combinatorial proofs of two truncated theta series theorems","volume":"160","author":"Ballantine","year":"2018","journal-title":"J. Combin. Theory Ser. 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Combin."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1007\/s11139-021-00544-2","article-title":"Generalizations of the truncated pentagonal number theorem results","volume":"59","author":"Kolitsch","year":"2022","journal-title":"Ramanujan J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1017\/S0013091522000347","article-title":"Truncated versions of three identities of Euler and Gauss","volume":"65","author":"Yao","year":"2022","journal-title":"Proc. Edinb. Math. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1007\/s13398-023-01436-4","article-title":"Truncated sums for certain restricted partition functions and transformation formulas for basic hypergeometric series","volume":"117","author":"Yao","year":"2023","journal-title":"Rev. R. Acad. Cienc. Exactas F\u00eds. Nat. Ser. A Math. RACSAM"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jcta.2014.10.005","article-title":"A truncated Jacobi triple product theorem","volume":"130","author":"Yee","year":"2016","journal-title":"J. Combin. Theory Ser. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1007\/s13398-023-01412-y","article-title":"A generalized truncated sums of Jacobi triple product series and some related truncated theorems","volume":"117","author":"Li","year":"2023","journal-title":"Rev. R. Acad. Cienc. Exactas F\u00eds. Nat. Ser. A Math. RACSAM"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.jcta.2014.10.004","article-title":"Proofs of two conjectures on truncated series","volume":"130","author":"Mao","year":"2015","journal-title":"J. Combin. Theory Ser. 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