{"paper":{"title":"Set Reconstruction on the Hypercube","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luke Pebody","submitted_at":"2016-07-19T17:45:05Z","abstract_excerpt":"Given an action of a group $G$ on a set $S$, the $k$-deck of a subset $T$ of $S$ is the multiset of all subsets of $T$ of size $k$, each given up to translation by $G$. For a given subset $T$, the {\\em reconstruction number} of $T$ is the minimum $k$ such that the $k$-deck uniquely identifies $T$ up to translation by $G$, and the {\\em reconstruction number} of the action $G:S$ is the maximum reconstruction number of any subset of $S$. The concept of reconstruction number extends naturally to multisubsets $T$ of $S$ and in~\\cite{CPC:257539}, the author calculated the multiset-reconstruction num"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05675","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"}