Briefly Recalling Some Antecedents of Standards-Based Reform and Standardized Assessment in American Mathematics Education - Darrow, Brian (Journal of Mathematics Education at Teachers College, 2023)
Keywords: dept.mat; peer-reviewed

On Tight 6-Cycle Decompositions of Complete 3-Uniform Multi-Hypergraphs - Bandell, Jessica A.; Bunge, Ryan C.; Darrow, Brian D.; El-Zanati, Saad I.; Mountain, Claire E.; Neiburger, Levi (Springer Proceedings in Mathematics and Statistics, 2025)
The λ-fold complete 3-uniform hypergraph on v vertices has the edge multiset consisting of λ copies of each 3-element subset of its vertex set. A tight 6-cycle, denoted TC6, is a hypergraph with vertex set {a,b,c,d,e,f} and edge set {{a,b,c},{b,c,d},{c,d,e},{d,e,f},{e,f,a},{f,a,b}}. We give necessary and sufficient conditions on v for the existence of a TC6-decomposition of the λ-fold complete 3-uniform hypergraph on v vertices for any positive integer λ. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
Keywords: 3-uniform; Combinatorics; Computer science; Decomposition; Hypergraph; Mathematics; Multi-hypergraph; dept.mat