{"paper":{"title":"On the Sprague-Grundy function of compound games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Endre Boros, Kazuhisa Makino, Levi Kitrossky, Vladimir Gurvich","submitted_at":"2019-03-19T17:48:39Z","abstract_excerpt":"The classical game of {\\sc Nim} can be naturally extended and played on an arbitrary hypergraph $\\cH \\subseteq 2^V \\setminus \\{\\emptyset\\}$ whose vertices $V = \\{1, \\ldots, n\\}$ correspond to piles of stones. By one move a player chooses an edge $H$ of $\\cH$ and reduces arbitrarily all piles $i \\in H$. In 1901 Bouton solved the classical {\\sc Nim} for which $\\cH = \\{\\{1\\}, \\ldots, \\{n\\}\\}$. In 1910 Moore introduced and solved a more general game $k$-{\\sc Nim}, for which $\\cH = \\{H \\subseteq V \\mid |H| \\leq k\\}$, where $1 \\leq k < n$. In 1980 Jenkyns and Mayberry obtained an explicit formula fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08138","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"}