{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:56Z","timestamp":1753893836639,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In 2004, J.-C. Aval, F. Bergeron and N. Bergeron studied the algebra of diagonally quasi-symmetric functions $\\operatorname{\\mathsf{DQSym}}$ in the ring $\\mathbb{Q}[\\mathbf{x},\\mathbf{y}]$ with two sets of variables. They made conjectures on the structure of the quotient $\\mathbb{Q}[\\mathbf{x},\\mathbf{y}]\/\\langle\\operatorname{\\mathsf{DQSym}}^+\\rangle$, which is a quasi-symmetric analogue of the diagonal harmonic polynomials. In this paper, we construct a Hilbert basis for this quotient when there are infinitely many variables i.e. $\\mathbf{x}=x_1,x_2,\\dots$ and $\\mathbf{y}=y_1,y_2,\\dots$. Then we apply this construction to the case where there are finitely many variables, and compute the second column of its Hilbert matrix.<\/jats:p>","DOI":"10.37236\/6658","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:51:31Z","timestamp":1578671491000},"source":"Crossref","is-referenced-by-count":1,"title":["Ideals and Quotients of Diagonally Quasi-Symmetric Functions"],"prefix":"10.37236","volume":"24","author":[{"given":"Shu Xiao","family":"Li","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,7,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p3\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:51:25Z","timestamp":1579236685000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i3p3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,14]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/6658","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,7,14]]},"article-number":"P3.3"}}