{"paper":{"title":"Subtraction games with FES sets of size 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Danny Sleator, Marla Slusky","submitted_at":"2012-01-16T16:01:43Z","abstract_excerpt":"This paper extends the work done by Angela Siegel on subtraction games in which the subtraction set is N \\ X for some finite set X. Siegel proves that for any finite set X, the G-sequence is ultimately arithmetic periodic, and that if |X| = 1 or 2, then it is purely arithmetic periodic. This note proves that if |X| = 3 then the G-sequence is purely arithmetic periodic. It is known that for |X| \\geq 4 the sequence is not always purely arithmetic periodic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3299","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":""},"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"}