{"paper":{"title":"Sprague-Grundy Function of Symmetric Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Endre Boros, Kazuhisa Makino, Nhan Bao Ho, Peter Mursic, Vladimir Gurvich","submitted_at":"2018-04-01T02:30:05Z","abstract_excerpt":"We consider a generalization of the classical game of $NIM$ called hypergraph $NIM$. Given a hypergraph $\\cH$ on the ground set $V = \\{1, \\ldots, n\\}$ of $n$ piles of stones, two players alternate in choosing a hyperedge $H \\in \\cH$ and strictly decreasing all piles $i\\in H$. The player who makes the last move is the winner. Recently it was shown that for many classes of hypergraphs the Sprague-Grundy function of the corresponding game is given by the formula introduced originally by Jenkyns and Mayberry (1980). In this paper we characterize symmetric hypergraphs for which the Sprague-Grundy f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01859","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"}