{"paper":{"title":"Stability for Take-Away Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sherry Sarkar, Simon Rubinstein-Salzedo","submitted_at":"2018-09-20T17:34:15Z","abstract_excerpt":"In this paper, we study a family of take-away games called $\\alpha$-tag, parametrized by a real number $\\alpha\\ge 1$. We show that for any given $\\alpha$, there is a half-open interval $I_\\alpha$ containing $\\alpha$ such that the set of losing positions for $\\alpha$-tag is the same as the set of losing positions for $\\beta$-tag if and only if $\\beta\\in I_\\alpha$. We then end with some results and conjectures on the nature of these intervals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07749","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"}