{"paper":{"title":"Partizan Kayles and Misere Invertibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rebecca Milley","submitted_at":"2013-09-06T13:17:54Z","abstract_excerpt":"The impartial combinatorial game Kayles is played on a row of pins, with players taking turns removing either a single pin or two adjacent pins. A natural partizan variation is to allow one player to remove only a single pin and the other only a pair of pins. This paper develops a complete solution for \"Partizan Kayles\" under misere play, including the misere monoid all possible sums of positions, and discusses its significance in the context of misere invertibility: the universe of Partizan Kayles contains a position whose additive inverse is not its negative, and, moreover, this position is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1631","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"}