{"paper":{"title":"Connectedness in Friends-and-Strangers Graphs of Spiders and Complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan Lee","submitted_at":"2022-10-05T06:43:43Z","abstract_excerpt":"Let $X$ and $Y$ be two graphs with vertex set $[n]$. Their friends-and-strangers graph $\\mathsf{FS}(X,Y)$ is a graph with vertices corresponding to elements of the group $S_n$, and two permutations $\\sigma$ and $\\sigma'$ are adjacent if they are separated by a transposition $\\{a,b\\}$ such that $a$ and $b$ are adjacent in $X$ and $\\sigma(a)$ and $\\sigma(b)$ are adjacent in $Y$. Specific friends-and-strangers graphs such as $\\mathsf{FS}(\\mathsf{Path}_n,Y)$ and $\\mathsf{FS}(\\mathsf{Cycle}_n,Y)$ have been researched, and their connected components have been enumerated using various equivalence rel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.04768","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.04768/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}