{"paper":{"title":"On additive properties of sets defined by the Thue-Morse word","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.CO","authors_text":"Luca Q. Zamboni, Michelangelo Bucci, Neil Hindman, Svetlana Puzynina","submitted_at":"2013-01-22T09:20:07Z","abstract_excerpt":"In this paper we study some additive properties of subsets of the set $\\nats$ of positive integers: A subset $A$ of $\\nats$ is called {\\it $k$-summable} (where $k\\in\\ben$) if $A$ contains $\\textstyle \\big{\\sum_{n\\in F}x_n | \\emp\\neq F\\subseteq {1,2,...,k\\} \\big}$ for some $k$-term sequence of natural numbers $x_1<x_2 < ... < x_k$. We say $A \\subseteq \\nats$ is finite FS-big if $A$ is $k$-summable for each positive integer $k$. We say is $A \\subseteq \\nats$ is infinite FS-big if for each positive integer $k,$ $A$ contains ${\\sum_{n\\in F}x_n | \\emp\\neq F\\subseteq \\nats and #F\\leq k}$ for some in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5118","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"}