{"paper":{"title":"Hankel determinants of weighted binary sums of digits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Bartosz Sobolewski, Maciej Ulas","submitted_at":"2026-07-10T12:58:11Z","abstract_excerpt":"Let $s_\\mathbf{w}$ be the weighted binary sum-of-digits function associated with an arbitrary sequence of complex weights $\\mathbf{w}=(w_j)_{j\\geq 0}$. We investigate Hankel determinants $\\mathcal{H}_\\mathbf{w}(n) = \\det [s_{\\mathbf{w}}(i+j)]_{0\\leq i,j<n}$ and derive a general recursion that allows us to effectively compute $\\mathcal{H}_\\mathbf{w}(n)$ for all $n$. Applying it to the ordinary binary sum-of-digits, that is, $w_j=1$, we express $\\mathcal{H}_\\mathbf{w}(n)$ in a closed form for several sequences of indices, including the remarkably simple $$ \\mathcal{H}_\\mathbf{w}(\\lceil 2^{k+2}/3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09376","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.09376/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}