{"paper":{"title":"System of unbiased representatives for a collection of bicolorings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Niranjan Balachandran, Rogers Mathew, Sudebkumar Prasant Pal, Tapas Kumar Mishra","submitted_at":"2017-04-25T14:33:34Z","abstract_excerpt":"Let $\\mathcal{B}$ denote a set of bicolorings of $[n]$, where each bicoloring is a mapping of the points in $[n]$ to $\\{-1,+1\\}$.\n  For each $B \\in \\mathcal{B}$, let $Y_B=(B(1),\\ldots,B(n))$.\n  For each $A \\subseteq [n]$, let $X_A \\in \\{0,1\\}^n$ denote the incidence vector of $A$.\n  A non-empty set $A$ is said to be an `unbiased representative' for a bicoloring $B \\in \\mathcal{B}$ if $\\left\\langle X_A,Y_B\\right\\rangle =0$.\n  Given a set $\\mathcal{B}$ of bicolorings, we study the minimum cardinality of a family $\\mathcal{A}$ consisting of subsets of $[n]$ such that every bicoloring in $\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07716","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"}