{"paper":{"title":"Mis\\`ere Cricket Pitch","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ethan J. Saunders, Richard J. Nowakowski","submitted_at":"2024-11-26T15:27:43Z","abstract_excerpt":"Mis\\`ere games in general have little algebraic structure, but if the games under consideration have properties then some algebraic structure re-appears. In 2023, the class of Blocking games was identified. Mis\\`ere Cricket Pitch was suggested as a problem at the Games-at-Dal-2023 Workshop, and is the first game in this class to be studied. Normal play Cricket Pitch was analyzed in 2011.\n  The game involves flattening `bumps' with a roller. The main reduction of normal play, reducing every bump by $2$, is not applicable in mis\\`ere play.\n  In this paper, we find the outcomes of single (linear)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17518","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.17518/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}