{"paper":{"title":"Antiassociative Groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"David Hobby, Donald Silberger, Milton Braitt","submitted_at":"2014-10-28T02:55:51Z","abstract_excerpt":"Given a groupoid $< G, \\star >$, and $k \\geq 3$, we say that $G$ is antiassociative iff for all $x_1, x_2, x_3 \\in G$, $(x_1 \\star x_2) \\star x_3$ and $x_1 \\star (x_2 \\star x_3)$ are never equal. Generalizing this, $< G, \\star >$ is $k$-antiassociative iff for all $x_1, x_2, ... x_k \\in G$, any two distinct expressions made by putting parentheses in $x_1 \\star x_2 \\star x_3 \\star ...x_k$ are never equal.\n  We prove that for every $k \\geq 3$, there exist finite groupoids that are $k$-antiassociative. We then generalize this, investigating when other pairs of groupoid terms can be made never equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7501","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"}