{"paper":{"title":"On generalized Howell designs with block size three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrea C. Burgess, Eric Mendelsohn, Peter Danziger, R. Julian R. Abel, Robert F. Bailey","submitted_at":"2015-01-11T22:20:58Z","abstract_excerpt":"In this paper, we examine a class of doubly resolvable combinatorial objects. Let $t, k, \\lambda, s$ and $v$ be nonnegative integers, and let $X$ be a set of $v$ symbols. A generalized Howell design, denoted $t$-$GHD_{k}(s,v;\\lambda)$, is an $s\\times s$ array, each cell of which is either empty or contains a $k$-set of symbols from $X$, called a block, such that: (i) each symbol appears exactly once in each row and in each column (i.e.\\ each row and column is a resolution of $X$); (ii) no $t$-subset of elements from $X$ appears in more than $\\lambda$ cells. Particular instances of the paramete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02502","kind":"arxiv","version":3},"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"}