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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.5118","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T09:20:07Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"ea2e772c8eae1aa1350bdd67c41c1b9db424ace366c61bf4725e4dd1e9379f67","abstract_canon_sha256":"95822656c8e7aac7076e65ed9d5445406ddf801c33aad863142f84d83c47bb9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:04.817773Z","signature_b64":"17PIUBQ/9Bx2oPJb6jJ322c/2EuVjd7YfonwEI9uQqSOaw6pK06MDUQCBbIxe0tDEPAsvo7NklO9SzafOzxGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3892620c25a53aee3679514301d85c7a1b5908391e952a2846a78172a8ac6235","last_reissued_at":"2026-05-18T03:32:04.817211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:04.817211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $k$. 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