{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:14Z","timestamp":1753893854630,"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>Stanley defined a partition function $t(n)$ as the number of partitions $\\lambda$ of $n$ such that the number of odd parts of $\\lambda$ is congruent to the number of odd parts of the conjugate partition $\\lambda'$ modulo $4$. We show that $t(n)$ equals the number of partitions of $n$ with an even number of hooks of even length. We derive a closed-form formula for the generating function for the numbers $p(n)-t(n)$.  As a consequence, we see that $t(n)$ has the same parity as the ordinary partition function $p(n)$. A simple combinatorial explanation of this fact is also provided.<\/jats:p>","DOI":"10.37236\/480","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:10:07Z","timestamp":1578697807000},"source":"Crossref","is-referenced-by-count":1,"title":["On Stanley's Partition Function"],"prefix":"10.37236","volume":"17","author":[{"given":"William Y. C.","family":"Chen","sequence":"first","affiliation":[]},{"given":"Kathy Q.","family":"Ji","sequence":"additional","affiliation":[]},{"given":"Albert J. W.","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,9,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1n31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1n31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:27:31Z","timestamp":1579285651000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1n31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9,1]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/480","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,9,1]]},"article-number":"N31"}}