{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,9]],"date-time":"2025-11-09T07:46:24Z","timestamp":1762674384959,"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>The index of a Lie algebra is an important algebraic invariant.\u00a0 In 2000, Vladimir Dergachev and Alexandre Kirillov\u00a0 defined seaweed subalgebras of $\\mathfrak{gl}_n$ (or $\\mathfrak{sl}_n$) and provided a formula for the index of a seaweed algebra using a certain graph, a so called meander.\r\nIn a recent paper, Vincent Coll, Andrew Mayers, and Nick Mayers defined a new statistic for partitions, namely\u00a0 the index of a partition, which arises from seaweed Lie algebras of type A. At the end of their paper, they presented an interesting conjecture, which involves integer partitions into odd parts. Motivated by their work, in this paper, we exploit various index statistics and the index weight generating functions for partitions.\u00a0 In particular, we examine their conjecture by considering the generating function for partitions into odd parts.\u00a0 We will also reprove another result\u00a0 from their paper using generating functions.<\/jats:p>","DOI":"10.37236\/9054","type":"journal-article","created":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T00:34:26Z","timestamp":1582245266000},"source":"Crossref","is-referenced-by-count":2,"title":["Index of Seaweed Algebras and Integer Partitions"],"prefix":"10.37236","volume":"27","author":[{"given":"Seunghyun","family":"Seo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ae Ja","family":"Yee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,2,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p47\/8034","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p47\/8034","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T00:34:27Z","timestamp":1582245267000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p47"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,21]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9054","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,2,21]]},"article-number":"P1.47"}}