{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:43Z","timestamp":1753893823166,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Closed forms for $f_{\\lambda,i} (q) := \\sum_{\\tau \\in SYT(\\lambda) : des(\\tau) = i} q^{maj(\\tau)}$, the distribution of the major index over standard Young tableaux of given shapes and specified number of descents, are established for a large collection of $\\lambda$ and $i$. Of particular interest is the family that gives a positive answer to a question of Sagan and collaborators. All formulas established in the paper are unimodal, most by a result of Kirillov and Reshetikhin. Many can be identified as specializations of Schur functions via the Jacobi-Trudi identities. If the number of arguments is sufficiently large, it is shown that any finite principal specialization of any Schur function $s_\\lambda(1,q,q^2,\\dots,q^{n-1})$ has a combinatorial realization as the distribution of the major index over a given set of tableaux.<\/jats:p>","DOI":"10.37236\/8585","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T06:05:10Z","timestamp":1578636310000},"source":"Crossref","is-referenced-by-count":1,"title":["Families of Major Index Distributions: Closed Forms and Unimodality"],"prefix":"10.37236","volume":"26","author":[{"given":"William J.","family":"Keith","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,9,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p58\/7919","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p58\/7919","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:08:15Z","timestamp":1579234095000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i3p58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,27]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,7,4]]}},"URL":"https:\/\/doi.org\/10.37236\/8585","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,9,27]]},"article-number":"P3.58"}}