{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:38Z","timestamp":1753893818570,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $n\\ge 1$ be an integer and let $B_{n}$ denote the hyperoctahedral group of rank $n$. The group $B_{n}$ acts on the polynomial ring $Q[x_{1},\\dots,x_{n},y_{1},\\dots,y_{n}]$ by signed permutations simultaneously on both of the sets of variables $x_{1},\\dots,x_{n}$ and $y_{1},\\dots,y_{n}.$ The invariant ring\u00a0$M^{B_{n}}:=Q[x_{1},\\dots,x_{n},y_{1},\\dots,y_{n}]^{B_{n}}$ \u00a0is the ring of diagonally signed-symmetric polynomials. In this article, we provide an explicit free basis of $M^{B_{n}}$ as a module over the ring of symmetric polynomials on both of the sets of variables $x_{1}^{2},\\dots, x^{2}_{n}$ and\u00a0 $y_{1}^{2},\\dots, y^{2}_{n}$ using signed descent monomials. <\/jats:p>","DOI":"10.37236\/3224","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:11:21Z","timestamp":1578687081000},"source":"Crossref","is-referenced-by-count":0,"title":["A Basis for the Diagonally Signed-Symmetric Polynomials"],"prefix":"10.37236","volume":"20","author":[{"given":"Jos\u00e9 Manuel","family":"G\u00f3mez","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,12,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p36\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p36\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T06:10:18Z","timestamp":1579241418000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i4p36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,20]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/3224","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,12,20]]},"article-number":"P36"}}