{"paper":{"title":"Bernoulli trials of fixed parity, random and randomly oriented graphs","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christos Pelekis","submitted_at":"2013-12-23T11:27:19Z","abstract_excerpt":"Suppose you can color $n$ \\emph{biased} coins with $n$ colors, all coins having the same bias. It is forbidden to color both sides of a coin with the same color, but all other colors are allowed. Let $X$ be the number of different colors after a toss of the coins. We present a method to obtain an upper bound on a median of $X$. Our method is based on the analysis of the probability distribution of the number of vertices with even in-degree in graphs whose edges are given random orientations. Our analysis applies to the distribution of the number of vertices with odd degree in random sub-graphs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6524","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"}