{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:03Z","timestamp":1753893843752,"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>We introduce and develop a two-parameter chromatic symmetric function for a simple graph $G$ over the field of rational functions in $q$ and $t,\\,{\\Bbb Q}(q,t)$.  We derive its expansion in terms of the monomial symmetric functions, $m_{\\lambda}$, and present various correlation properties which exist between the two-parameter chromatic symmetric function and its corresponding graph. Additionally, for the complete graph $G$ of order $n$, its corresponding two-parameter chromatic symmetric function is the Macdonald polynomial $Q_{(n)}$.  Using this, we develop graphical analogues for the expansion formulas of the two-row Macdonald polynomials and the two-row Jack symmetric functions. Finally, we introduce the \"complement\" of this new function and explore some of its properties.<\/jats:p>","DOI":"10.37236\/940","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:51:43Z","timestamp":1578718303000},"source":"Crossref","is-referenced-by-count":0,"title":["A Two Parameter Chromatic Symmetric Function"],"prefix":"10.37236","volume":"14","author":[{"given":"Ellison-Anne","family":"Williams","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,2,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r22\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r22\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:04:25Z","timestamp":1579320265000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,2,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/940","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,2,12]]},"article-number":"R22"}}