{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T19:31:21Z","timestamp":1773257481376,"version":"3.50.1"},"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 completely characterize the appearance of Schur functions corresponding to partitions of the form $\\nu = (1^a, b)$ (hook shapes) in the Schur function expansion of the plethysm of two Schur functions, $$s_\\lambda[s_\\mu] = \\sum_{\\nu} a_{\\lambda, \\mu, \\nu} s_\\nu.$$  Specifically, we show that no Schur functions corresponding to hook shapes occur unless $\\lambda$ and $\\mu$ are both hook shapes and give a new proof of a result of Carbonara, Remmel and Yang that a single hook shape occurs in the expansion of the plethysm $s_{(1^c, d)}[s_{(1^a, b)}]$. We also consider the problem of adding a row or column so that $\\nu$ is of the form $(1^a,b,c)$ or $(1^a, 2^b, c)$.  This proves considerably more difficult than the hook case and we discuss these difficulties while deriving explicit formulas for a special case. <\/jats:p>","DOI":"10.37236\/1764","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:23:35Z","timestamp":1578720215000},"source":"Crossref","is-referenced-by-count":10,"title":["The Plethysm $s_\\lambda[s_\\mu]$ at Hook and Near-Hook Shapes"],"prefix":"10.37236","volume":"11","author":[{"given":"T. M.","family":"Langley","sequence":"first","affiliation":[]},{"given":"J. B.","family":"Remmel","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,1,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:04:55Z","timestamp":1579323895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1764","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1,23]]},"article-number":"R11"}}