{"paper":{"title":"Diamond-colored distributive lattices, move-minimizing games, and fundamental Weyl symmetric functions: The type $\\mathsf{A}$ case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elizabeth A. Donovan, Robert G. Donnelly, Timothy A. Schroeder","submitted_at":"2017-02-02T19:25:03Z","abstract_excerpt":"We present some elementary but foundational results concerning diamond-colored modular and distributive lattices and connect these structures to certain one-player combinatorial \"move-minimizing games,\" in particular, a so-called \"domino game.\" The objective of this game is to find, if possible, the least number of \"domino moves\" to get from one partition to another, where a domino move is, with one exception, the addition or removal of a domino-shaped pair of tiles. We solve this domino game by demonstrating the somewhat surprising fact that the associated \"game graphs\" coincide with a well-k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00806","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"}