{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:44Z","timestamp":1753893824604,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this brief note, we give two partition statistics which explain the following partition congruences:  \\begin{align*}  b(5n+4) &amp;\\equiv 0 \\pmod{5}, \\\\  b(7n+a) &amp;\\equiv 0 \\pmod{7}, \\text{if $a=2$, $3$, $4$, or $6$}.   \\end{align*}  Here, $b(n)$ is the number of $4$-color partitions of $n$ with colors $r$, $y$, $o$, and $b$ subject to the restriction that the colors $o$ and $b$ appear only in even parts.<\/jats:p>","DOI":"10.37236\/615","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:46:45Z","timestamp":1578714405000},"source":"Crossref","is-referenced-by-count":8,"title":["Partition Statistics for Cubic Partition Pairs"],"prefix":"10.37236","volume":"18","author":[{"given":"Byungchan","family":"Kim","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,6,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p128\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p128\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:11:02Z","timestamp":1579302662000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p128"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/615","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,6,14]]},"article-number":"P128"}}