{"paper":{"title":"There are $(r+1)(r+2)(2r+3)(r^2+3r+5)$ Ways For the Four Teams of a World Cup Group to Each Have $r$ Goals For and $r$ Goals Against [Thanks to the Soccer Analog of Prop. 4.6.19 of Richard Stanley's (Classic!) EC1]","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Doron Zeilberger, Shalosh B. Ekhad","submitted_at":"2014-07-08T00:57:10Z","abstract_excerpt":"This short tribute to the guru of Enumerative and Algebraic Combinatorics started out when one the authors(DZ) attended the Stanely@70 conference, that took place at the same time as the preliminary stage of the 2014 World Cup. It states a surprising application of an analog of Richard Stanley's famous theorem about the enumeration of magic squares to the enumeration of possible outcomes in a World Cup Group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1919","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"}