{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T09:13:29Z","timestamp":1775466809735,"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 provide direct proofs of product and coproduct formulae for Schur functions where the coefficients (Littlewood\u2013Richardson coefficients) are defined as counting puzzles. The product formula includes a second alphabet for the Schur functions, allowing in particular to recover formulae of [Molev\u2013Sagan '99] and [Knutson\u2013Tao '03] for factorial Schur functions.  The method is based on the quantum integrability of the underlying tiling model.<\/jats:p>","DOI":"10.37236\/101","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:36:29Z","timestamp":1578717389000},"source":"Crossref","is-referenced-by-count":16,"title":["Littlewood&amp;ndash;Richardson Coefficients and Integrable Tilings"],"prefix":"10.37236","volume":"16","author":[{"given":"Paul","family":"Zinn-Justin","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,1,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r12\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:14:21Z","timestamp":1579317261000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/101","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1,23]]},"article-number":"R12"}}