{"paper":{"title":"A digit reversal property for Stern polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lukas Spiegelhofer","submitted_at":"2016-10-01T09:20:46Z","abstract_excerpt":"We consider the following polynomial generalization of Stern's diatomic series: let $s_1(x,y)=1$, and for $n\\geq 1$ set $s_{2n}(x,y)=s_n(x,y)$ and $s_{2n+1}(x,y)=x\\,s_n(x,y)+y\\,s_{n+1}(x,y)$. The coefficient $[x^iy^j]s_n(x,y)$ is the number of hyperbinary expansions of $n-1$ with exactly $i$ occurrences of the digit $\\mathtt 2$ and $j$ occurrences of $\\mathtt 0$. We prove that the polynomials $s_n$ are invariant under \\emph{digit reversal}, that is, $s_n=s_{n^R}$, where $n^R$ is obtained from $n$ by reversing the binary expansion of $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00108","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"}