{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:57:38Z","timestamp":1775465858621,"version":"3.50.1"},"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>The nonelliptic $\\mathsf{A_2}$-webs with $k$ \"$+$''s on the top boundary and $3n-2k$ \"$-$''s on the bottom boundary combinatorially model the space $\\mathsf{Hom}_{\\mathfrak{sl}_3}(\\mathsf{V}^{\\otimes (3n-2k)}, \\mathsf{V}^{\\otimes k})$ of\u00a0 $\\mathfrak{sl}_3$-module maps on tensor powers of the natural 3-dimensional $\\mathfrak{sl}_3$-module $\\mathsf{V}$,\u00a0 and they have connections with the combinatorics ofSpringer varieties. Petersen, Pylyavskyy, and Rhodes showed\u00a0 that the set of such\u00a0 $\\mathsf{A_2}$-webs and the set of\u00a0 semistandard tableaux of shape $(3^n)$ and type $\\{1^2,\\dots,k^2,k+1,\\dots, 3n-k\\}$ have the same cardinalities. In this work, we use the $\\sf{m}$-diagrams introduced by Tymoczko and the Robinson-Schensted correspondence to construct an explicit bijection, different from the one given by Russell, between these two sets.\u00a0 In establishing our result, we show that the pair of standard\u00a0 tableaux constructed using the notion of path depth is the same as the pair constructed from applying the Robinson-Schensted correspondence to a $3\\,2\\,1$-avoiding permutation.\u00a0 We also obtain a bijection between such pairs of standard tableaux and Westbury's $\\mathsf{A_2}$ flow diagrams.<\/jats:p>","DOI":"10.37236\/3936","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:04:57Z","timestamp":1578704697000},"source":"Crossref","is-referenced-by-count":1,"title":["The Combinatorics of $\\mathsf{A_2}$-Webs"],"prefix":"10.37236","volume":"21","author":[{"given":"Georgia","family":"Benkart","sequence":"first","affiliation":[]},{"given":"Soojin","family":"Cho","sequence":"additional","affiliation":[]},{"given":"Dongho","family":"Moon","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,5,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p25\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p25\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:59:34Z","timestamp":1579258774000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i2p25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,9]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/3936","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,9]]},"article-number":"P2.25"}}