The existence of designs
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2014
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| _version_ | 1866913587738443776 |
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| author | Keevash, Peter |
| author_facet | Keevash, Peter |
| contents | We prove the existence conjecture for combinatorial designs, answering a question of Steiner from 1853. More generally, we show that the natural divisibility conditions are sufficient for clique decompositions of simplicial complexes that satisfy a certain pseudorandomness condition. As a further generalisation, we obtain the same conclusion only assuming an extendability property and the existence of a robust fractional clique decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1401_3665 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | The existence of designs Keevash, Peter Combinatorics We prove the existence conjecture for combinatorial designs, answering a question of Steiner from 1853. More generally, we show that the natural divisibility conditions are sufficient for clique decompositions of simplicial complexes that satisfy a certain pseudorandomness condition. As a further generalisation, we obtain the same conclusion only assuming an extendability property and the existence of a robust fractional clique decomposition. |
| title | The existence of designs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1401.3665 |