{"paper":{"title":"Generalized Gray codes with prescribed ends","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Petr Gregor, Tom\\'a\\v{s} Dvo\\v{r}\\'ak, V\\'aclav Koubek","submitted_at":"2016-03-29T16:16:35Z","abstract_excerpt":"An $n$-bit Gray code is a sequence of all $n$-bit strings such that consecutive strings differ in a single bit. It is well-known that given $\\alpha,\\beta\\in\\{0,1\\}^n$, an $n$-bit Gray code between $\\alpha$ and $\\beta$ exists iff the Hamming distance $d(\\alpha,\\beta)$ of $\\alpha$ and $\\beta$ is odd. We generalize this classical result to $k$ pairwise disjoint pairs $\\alpha_i, \\beta_i\\in\\{0,1\\}^n$: if $d(\\alpha_i,\\beta_i)$ is odd for all $i$ and $k<n$, then the set of all $n$-bit strings can be partitioned into $k$ sequences such that the $i$-th sequence leads from $\\alpha_i$ to $\\beta_i$ and co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08827","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"}