{"paper":{"title":"Characterizations of biselective operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Gergely Kiss, Jimmy Devillet","submitted_at":"2018-06-06T09:02:41Z","abstract_excerpt":"Let $X$ be a nonempty set and let $i,j \\in \\{1,2,3,4\\}$. We say that a binary operation $F:X^2\\to X$ is $(i,j)$-selective if $$ F(F(x_1,x_2),F(x_3,x_4))~=~F(x_i,x_j), $$ for all $x_1,x_2,x_3,x_4\\in X$. In this paper we provide characterizations of the class of $(i,j)$-selective operations. We also investigate some subclasses by adding algebraic properties such as associativity or bisymmetry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02073","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"}