{"paper":{"title":"Constructions and uses of incomplete pairwise balanced designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Esther R. Lamken, Peter J. Dukes","submitted_at":"2018-09-20T21:11:57Z","abstract_excerpt":"We give explicit constructions for incomplete pairwise balanced designs IPBD$((v;w),K)$, or, equivalently, edge-decompositions of a difference of two cliques $K_v \\setminus K_w$ into cliques whose sizes belong to the set $K$. Our constructions produce such designs whenever $v$ and $w$ satisfy the usual divisibility conditions, have ratio $v/w$ bounded away from the smallest value in $K$ minus one, say $v/w > k-1+\\epsilon$, for $k =\\min K$ and $\\epsilon>0$, and are sufficiently large (depending on $K$ and $\\epsilon$). As a consequence, some new results are obtained on many related designs, incl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07866","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"}