{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T01:38:52Z","timestamp":1774489132169,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $b_\\ell(n)$ denote the number of $\\ell$-regular partitions of $n$. Congruences properties modulo powers of $2$ for $b_4(n)$ were considered subsequently by Andrews-Hirschhorn-Sellers, Chen, Cui-Gu, Xia, Dai, and Ballantine-Merca. In this paper, we present an approach which can be utilized to prove the ``self-similar'' congruence property satisfied by the generating function of $b_4(n)$. As an immediate consequence, one can obtain dozens of congruence families modulo powers of $2$ enjoyed by $b_4(n)$. These results not only generalize some previous results, but also can be viewed as a supplement to Keith and Zanello's comprehensive study of the congruence properties for $\\ell$-regular partition functions. Finally, we also pose several conjectures on congruence families, internal congruence families and self-similar congruence properties for $4$-, $8$- and $16$-regular partition functions.<\/jats:p>","DOI":"10.37236\/11919","type":"journal-article","created":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T09:33:47Z","timestamp":1726824827000},"source":"Crossref","is-referenced-by-count":2,"title":["Congruence Properties Modulo Powers of $2$ for $4$-Regular Partitions"],"prefix":"10.37236","volume":"31","author":[{"given":"Julia Q. D.","family":"Du","sequence":"first","affiliation":[]},{"given":"Dazhao","family":"Tang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2024,9,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i3p32\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i3p32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T09:33:48Z","timestamp":1726824828000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i3p32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,20]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/11919","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,20]]},"article-number":"P3.32"}}