The existence of designs II
By Peter Keevash. 2018
63 citations recorded by the source corpus.
We generalise the existence of combinatorial designs to the setting of subset sums in lattices with coordinates indexed by labelled faces of simplicial complexes. This general framework includes the problem of decomposing hypergraphs with extra edge data, such as colours and orders, and so incorporates a wide range of variations on the basic design problem, notably Baranyai-type generalisations, such as resolvable hypergraph designs, large sets of hypergraph designs and decompositions of designs by designs. Our method also gives approximate counting results, which is new for many structures whose existence was previously known, such as high dimensional permutations or Sudoku squares.
Subfields: Computer Vision and Pattern Recognition, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/46af42e6108a8589cffbf20bcbc97332d8e8ada8
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In Computer Vision and Pattern Recognition
In Discrete Mathematics and Combinatorics
- Deryk Osthus
- D. Kühn
- Allan Siu Lun Lo
- Matthew Kwan
- Stefan Glock
- Peter Keevash
- Richard Mycroft
- Yi Zhao
In Electrical and Electronic Engineering
Citations in the corpus
- The Existence of Designs via Iterative Absorption: Hypergraph 𝐹-designs for Arbitrary 𝐹 (2016, background): “This answers a question asked e.g. by Keevash [23].”
- Almost all Steiner triple systems have perfect matchings (2016, methodology): “However, the Steiner triple systems obtainable by Keevash’s construction comprise a negligible proportion of the set of Steiner triple systems, and a somewhat more delicate approach is required to study a uniformly random Steiner triple system.”