{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:09Z","timestamp":1753893849657,"version":"3.41.2"},"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>In this paper, we develop the Robinson-Schensted correspondence for the signed Brauer algebra. The Robinson-Schensted correspondence gives the bijection between the set of signed Brauer diagrams $d$ and the pairs of standard bi-dominotableaux of shape $\\lambda=(\\lambda_1,\\lambda_2)$ with $\\lambda_1=(2^{2f}),\\lambda_2 \\in \\overline{\\Gamma}_{f,r}$ where $\\overline{\\Gamma}_{f,r}=\\{ \\lambda | \\lambda\\vdash 2(n-2f)+|\\delta_r| {\\rm \\ whose } \\ 2{\\rm-core \\ is \\ \\delta_r, \\ } \\delta_r=(r,r-1,\\ldots,1,0)\\}$, for fixed $r\\geq 0$ and $0\\leq f \\leq \\left[{n\\over 2}\\right]$.  We also give the Robinson-Schensted for the signed Brauer algebra using the vacillating tableau which gives the bijection between the set of signed Brauer diagrams ${\\overline{V}_n}$ and the pairs of $d$-vacillating tableaux of shape $\\lambda \\in \\overline{\\Gamma}_{f,r}$ and $0\\leq f \\leq \\left[{n\\over 2}\\right]$. We derive the Knuth relations and the determinantal formula for the signed Brauer algebra by using the Robinson-Schensted correspondence for the standard bi-dominotableau whose core is $\\delta_{r}$, $r \\geq n-1$.<\/jats:p>","DOI":"10.37236\/967","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:49:28Z","timestamp":1578718168000},"source":"Crossref","is-referenced-by-count":2,"title":["Robinson-Schensted Correspondence for the Signed Brauer Algebras"],"prefix":"10.37236","volume":"14","author":[{"given":"M.","family":"Parvathi","sequence":"first","affiliation":[]},{"given":"A.","family":"Tamilselvi","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,7,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r49\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r49\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:02:14Z","timestamp":1579320134000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,7,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/967","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,7,19]]},"article-number":"R49"}}