{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:25Z","timestamp":1753893805988,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Because they play a role in our understanding of the symmetric group algebra,  Lie idempotents have received considerable attention.  The Klyachko  idempotent has attracted interest from combinatorialists, partly because its  definition involves the major index of permutations. For the symmetric group $S_n$, we look at the symmetric group algebra  with coefficients from the field of rational functions in $n$ variables  $q_1, \\ldots, q_n$.  In this setting, we can define an $n$-parameter  generalization of the Klyachko idempotent, and we show it is a Lie idempotent  in the appropriate sense.  Somewhat surprisingly, our proof that it is a Lie  element emerges from Stanley's theory of $P$-partitions. <\/jats:p>","DOI":"10.37236\/1878","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:17:38Z","timestamp":1578701858000},"source":"Crossref","is-referenced-by-count":2,"title":["$P$-Partitions and a Multi-Parameter Klyachko Idempotent"],"prefix":"10.37236","volume":"11","author":[{"given":"Peter","family":"McNamara","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christophe","family":"Reutenauer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2005,10,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2r21\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2r21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:40:22Z","timestamp":1579304422000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i2r21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,10,31]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2004,6,3]]}},"URL":"https:\/\/doi.org\/10.37236\/1878","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,10,31]]},"article-number":"R21"}}