{"paper":{"title":"Hindman's Coloring Theorem in arbitrary semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Boaz Tsaban, Gili Golan","submitted_at":"2013-03-14T20:44:41Z","abstract_excerpt":"Hindman's Theorem asserts that, for each finite coloring of the natural numbers, there are distinct natural numbers $a_1,a_2,\\dots$ such that all of the sums $a_{i_1}+a_{i_2}+\\dots+a_{i_m}$ ($m\\ge 1$, $i_1<i_2<\\dots<i_m$) have the same color.\n  The celebrated Galvin--Glazer proof of Hindman's Theorem and a classification of semigroups due to Shevrin, imply together that, for each finite coloring of each infinite semigroup $S$, there are distinct elements $a_1,a_2,\\dots$ of $S$ such that all but finitely many of the products $a_{i_1}a_{i_2}\\cdots a_{i_m}$ ($m\\ge 1$, $i_1<i_2<\\dots<i_m$) have th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3600","kind":"arxiv","version":2},"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"}