{"paper":{"title":"A combinatorial Hopf algebra for the boson normal ordering problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"Ali Chouria, Imad Eddine Bousbaa, Jean-Gabriel Luque","submitted_at":"2015-12-18T13:14:55Z","abstract_excerpt":"In the aim to understand the generalization of Stirling numbers occurring in the bosonic normal ordering problem, several combinatorial models have been proposed. In particular, Blasiak \\emph{et al.} defined combinatorial objects allowing to interpret the number of $S_{\\bf{r,s}}(k)$ appearing in the identity $(a^\\dag)^{r_n}a^{s_n}\\cdots(a^\\dag)^{r_1}a^{s_1}=(a^\\dag)^\\alpha\\displaystyle\\sum S_{\\bf{r,s}}(k)(a^\\dag)^k a^k$, where $\\alpha$ is assumed to be non-negative. These objects are used to define a combinatorial Hopf algebra which specializes to the enveloping algebra of the Heisenberg Lie a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05937","kind":"arxiv","version":2},"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"}