{"paper":{"title":"On the compatibility of binary sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bernardo N. B. de Lima, Harry Kesten, Maria Eul\\'alia Vares, Vladas Sidoravicius","submitted_at":"2012-04-14T19:09:50Z","abstract_excerpt":"An ordered pair of semi-infinite binary sequences $(\\eta,\\xi)$ is said to be compatible if there is a way of removing a certain number (possibly infinite) of ones from $\\eta$ and zeroes from $\\xi$, whichwould map both sequences to the same semi-infinite sequence. This notion was introduced by Peter Winkler, who also posed the following question: $\\eta$ and $\\xi$ being independent i.i.d. Bernoulli sequences with parameters $p^\\prime$ and $p$ respectively, does it exist $(p', p)$ so that the set of compatible pairs has positive measure? It is known that this does not happen for $p$ and $p^\\prime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3197","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"}