{"paper":{"title":"i-MARK: A New Subtraction Division Game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Eric Sopena (LaBRI)","submitted_at":"2015-09-14T16:57:57Z","abstract_excerpt":"Given two finite sets of integers $S\\subseteq\\NNN\\setminus\\{0\\}$ and $D\\subseteq\\NNN\\setminus\\{0,1\\}$,the impartial combinatorial game $\\IMARK(S,D)$ is played on a heap of tokens. From a heap of $n$ tokens, each player can moveeither to a heap of $n-s$ tokens for some $s\\in S$, or to a heap of $n/d$ tokensfor some $d\\in D$ if $d$ divides $n$.Such games can be considered as an integral variant of \\MARK-type games, introduced by Elwyn Berlekamp and Joe Buhlerand studied by Aviezri Fraenkel and Alan Guo, for which it is allowed to move from a heap of $n$ tokensto a heap of $\\lfloor n/d\\rfloor$ to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04199","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"}