The existence of designs via iterative absorption Article Swipe

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Conjecture Flexibility (engineering) Resilience (materials science) Clique Distribution (mathematics) Absorption (acoustics) Iterative method Degree (music) Mathematics Computer science Mathematical optimization Combinatorics Applied mathematics Statistics Materials science Physics Mathematical analysis Composite material Acoustics

Stefan Glock , Daniela Kühn , Allan Lo , Deryk Osthus ·

YOU? · · 2016 · Open Access · · OA: W2555546311

In a recent breakthrough, Keevash proved the Existence conjecture for combinatorial designs, which has its roots in the 19th century. We give a new proof, based on the method of iterative absorption. Our main result concerns $K^{(r)}_{q}$-decompositions of hypergraphs whose clique distribution fulfils certain uniformity criteria. These criteria offer considerable flexibility. This enables us to strengthen the results of Keevash as well as to derive a number of new results, for example a resilience version and minimum degree version.