{"paper":{"title":"Balances of $m$-bonacci words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Edita Pelantov\\'a, Karel B\\v{r}inda, Ond\\v{r}ej Turek","submitted_at":"2013-01-15T13:13:32Z","abstract_excerpt":"The $m$-bonacci word is a generalization of the Fibonacci word to the $m$-letter alphabet $\\mathcal{A} = {0,...,m-1}$. It is the unique fixed point of the Pisot--type substitution $ \\varphi_m: 0\\to 01, 1\\to 02, ..., (m-2)\\to0(m-1), and (m-1)\\to0$. A result of Adamczewski implies the existence of constants $c^{(m)}$ such that the $m$-bonacci word is $c^{(m)}$-balanced, i.e., numbers of letter $a$ occurring in two factors of the same length differ at most by $c^{(m)}$ for any letter $a\\in \\mathcal{A}$. The constants $c^{(m)}$ have been already determined for $m=2$ and $m=3$. In this paper we stu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3334","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"}