{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:34Z","timestamp":1753893814601,"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>Schur\u2013Weyl duality is a fundamental framework in combinatorial representation theory.\u00a0It intimately relates the irreducible representations of a group to the irreducible representations of its centralizer algebra.\u00a0We investigate the analog of Schur\u2013Weyl duality for the group of unipotent upper triangular matrices over a finite field.\u00a0 In this case, the character theory of these upper triangular matrices is \"wild\" or unattainable.\u00a0Thus we employ a generalization, known as supercharacter theory, that creates a striking variation on the character theory of the symmetric group with combinatorics built from set partitions.\u00a0In this paper, we present a combinatorial formula for calculating a restriction and induction of supercharacters based on statistics of set partitions and seashell inspired diagrams.\u00a0We use these formulas to create a graph that encodes the decomposition of a tensor space, and develop an analog of Young tableaux, known as shell tableaux, to index paths in this graph.\u00a0<\/jats:p>","DOI":"10.37236\/8241","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:07:55Z","timestamp":1578640075000},"source":"Crossref","is-referenced-by-count":0,"title":["Shell Tableaux: A Set Partition Analog of Vacillating Tableaux"],"prefix":"10.37236","volume":"26","author":[{"given":"Megan","family":"Ly","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,5,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p12\/7825","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p12\/7825","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:14:35Z","timestamp":1579234475000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i2p12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,3]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,4,5]]}},"URL":"https:\/\/doi.org\/10.37236\/8241","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,5,3]]},"article-number":"P2.12"}}