{"paper":{"title":"On generalized Kneser hypergraph colorings","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carsten Lange, Guenter M. Ziegler","submitted_at":"2005-04-29T19:51:43Z","abstract_excerpt":"In Ziegler (2002), the second author presented a lower bound for the chromatic numbers of hypergraphs $\\KG{r}{\\pmb s}{\\calS}$, \"generalized $r$-uniform Kneser hypergraphs with intersection multiplicities $\\pmb s$.\" It generalized previous lower bounds by Kriz (1992/2000) for the case ${\\pmb s}=(1,...,1)$ without intersection multiplicities, and by Sarkaria (1990) for $\\calS=\\tbinom{[n]}k$. Here we discuss subtleties and difficulties that arise for intersection multiplicities $s_i>1$:\n  1. In the presence of intersection multiplicities, there are two different versions of a \"Kneser hypergraph,\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504607","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"}