{"paper":{"title":"Profile and hereditary classes of ordered relational structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Djamila Oudrar, Maurice Pouzet","submitted_at":"2014-09-03T14:38:58Z","abstract_excerpt":"Let $\\mathfrak{C}$ be a class of finite combinatorial structures. The \\textit{profile} of $\\mathfrak{C}$ is the function $\\varphi_{\\mathfrak{C}}$ which counts, for every integer $n$, the number $\\varphi_{\\mathfrak{C}}(n)$ of members of $\\mathfrak{C}$ defined on $n$ elements, isomorphic structures been identified. The \\textit{generating function of} $\\mathfrak{C}$ is $\\mathcal {H}_{\\mathfrak{C}}(x):=\\sum_{n\\geqq 0}\\varphi_{\\mathfrak{C}}(n)x^{n}$. Many results about the behavior of the function $\\varphi_{\\mathfrak{C}}$ have been obtained. Albert and Atkinson have shown that the generating series"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1108","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}