{"paper":{"title":"On the additive complexity of a Thue-Morse like sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jin Chen, Wen Wu, Zhixiong Wen","submitted_at":"2018-02-10T15:44:57Z","abstract_excerpt":"In this paper, we study the additive complexity $\\rho^{+}_{\\mathbf{t}}(n)$ of a Thue-Morse like sequence $\\mathbf{t}=\\sigma^{\\infty}(0)$ with the morphism $\\sigma: 0\\to 01, 1\\to 12, 2\\to 20$. We show that $\\rho^{+}_{\\mathbf{t}}(n)=2\\lfloor\\log_2(n)\\rfloor+3$ for all integers $n\\geq 1$. Consequently, $(\\rho_{\\mathbf{t}}(n))_{n\\geq 1}$ is a $2$-regular sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03610","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"}