{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:58Z","timestamp":1753893838385,"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>This paper uses the theory of dual equivalence graphs to give explicit Schur expansions for several families of symmetric functions. We begin by giving a combinatorial definition of the modified Macdonald polynomials and modified Hall-Littlewood polynomials indexed by any diagram $\\delta \\subset {\\mathbb Z} \\times {\\mathbb Z}$, written as $\\widetilde H_{\\delta}(X;q,t)$ and $\\widetilde H_{\\delta}(X;0,t)$, respectively. We then give an explicit Schur expansion of $\\widetilde H_{\\delta}(X;0,t)$ as a sum over a subset of the Yamanouchi words, as opposed to the expansion using the charge statistic given in 1978 by Lascoux and Sch\u00fcztenberger. We further define the symmetric function $R_{\\gamma,\\delta}(X)$ as a refinement of $\\widetilde H_{\\delta}(X;0,t)$ and similarly describe its Schur expansion. We then analyze $R_{\\gamma,\\delta}(X)$ to determine the leading term of its Schur expansion. We also provide a conjecture towards the Schur expansion of $\\widetilde H_{\\delta}(X;q,t)$. To gain these results, we use a construction from the 2007 work of Sami Assaf to associate each Macdonald polynomial with a signed colored graph $\\mathcal{H}_\\delta$. In the case where a subgraph of $\\mathcal{H}_\\delta$ is a dual equivalence graph, we provide the Schur expansion of its associated symmetric function, yielding several corollaries. <\/jats:p>","DOI":"10.37236\/6732","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:58:36Z","timestamp":1578671916000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Schur Expansion of Hall-Littlewood and Related Polynomials via Yamanouchi Words"],"prefix":"10.37236","volume":"24","author":[{"given":"Austin","family":"Roberts","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p57\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p57\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:02:46Z","timestamp":1579237366000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i1p57"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1,20]]}},"URL":"https:\/\/doi.org\/10.37236\/6732","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,3,31]]},"article-number":"P1.57"}}