{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T11:51:26Z","timestamp":1771329086179,"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 profile of a relational structure $R$ is the function $\\phi_R$ which counts for every integer $n$ the number $\\phi_R(n)$, possibly infinite, of substructures of $R$ induced on the $n$-element subsets, isomorphic substructures being identified.\u00a0 If $\\phi_R$ takes only finite values, this is the Hilbert function of a graded algebra associated with $R$, the age algebra $KA(R)$, introduced by P. J. Cameron.  In this paper we give a closer look at this association, particularly when the relational structure $R$ admits a finite monomorphic decomposition. This setting still encompass well-studied graded commutative algebras like invariant rings of finite permutation groups, or the rings of quasi-symmetric polynomials. We prove that $\\phi_R$ is eventually a quasi-polynomial, this supporting the conjecture that, under mild assumptions on $R$, $\\phi_R$ is eventually a quasi-polynomial when it is bounded by some polynomial.<\/jats:p>","DOI":"10.37236\/2193","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:14:28Z","timestamp":1578719668000},"source":"Crossref","is-referenced-by-count":8,"title":["Some Relational Structures with Polynomial Growth and their Associated Algebras I: Quasi-Polynomiality of the Profile"],"prefix":"10.37236","volume":"20","author":[{"given":"Maurice","family":"Pouzet","sequence":"first","affiliation":[]},{"given":"Nicolas Marc","family":"Thi\u00e9ry","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,4,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:23:13Z","timestamp":1579260193000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i2p1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,9]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/2193","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,4,9]]},"article-number":"P1"}}