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010 a| 2023015045;

020 a| 9781470460242q| (paperback);

020 z| 9781470474447q| (pdf);

035 a| (WaSeSS)ssj0002864531;

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084 a| 05B05a| 05C51a| 05B30a| 05B40a| 05C702| msc;

100 1 a| Glock, Stefan.?| UNAUTHORIZED;

245 14 a| The existence of designs via iterative absorption: hypergraph F-designs for arbitrary Fh| [electronic resource] /c| Stefan Glock, Daniela Kuhn, Allan Lo, Deryk Osthus.;

260 a| Providence, RI :b| American Mathematical Society,c| 2023.;

300 a| v, 131 pages ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Volume 284;

500 a| "April 2023, Volume 284, Number 1406 (second of 6 numbers)";

504 a| Includes bibliographical references (pages 129-131).;

505 0 a| Notation -- Outline of the methods -- Decompositions of supercomplexes -- Tools -- Nibbles, boosting and greedy covers -- Vortices -- Absorbers -- Proof of the main theorems -- Covering down -- Achieving divisibility -- Recent developments.;

506 a| Available only to authorized users.;

520 a| "We solve the existence problem for F-designs for arbitrary r-uniform hypergraphs F. This implies that given any r-uniform hypergraph F, the trivially necessary divisibility conditions are sufficient to guarantee a decomposition of any sufficiently large complete r-uniform hypergraph into edge-disjoint copies of F, which answers a question asked e.g. by Keevash. The graph case r [equals] 2 was proved by Wilson in 1975 and forms one of the cornerstones of design theory. The case when F is complete corresponds to the existence of block designs, a problem going back to the 19th century, which was recently settled by Keevash. In particular, our argument provides a new proof of the existence of block designs, based on iterative absorption (which employs purely probabilistic and combinatorial methods). Our main result concerns decompositions of hypergraphs whose clique distribution fulfills certain regularity constraints. Our argument allows us to employ a 'regularity boosting' process which frequently enables us to satisfy these constraints even if the clique distribution of the original hypergraph does not satisfy them. This enables us to go significantly beyond the setting of quasirandom hypergraphs considered by Keevash. In particular, we obtain a resilience version and a decomposition result for hypergraphs of large minimum degree"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Block designs.=| ^A79266;

650 0 a| Decomposition (Mathematics)=| ^A65175;

650 0 a| Combinatorial packing and covering.=| ^A185216;

650 7 a| Combinatorics -- Designs and configurations -- Block designs.2| msc;

650 7 a| Combinatorics -- Graph theory -- Graph designs and isomomorphic decomposition.2| msc;

650 7 a| Combinatorics -- Designs and configurations -- Other designs, configurations.2| msc;

650 7 a| Combinatorics -- Designs and configurations -- Packing and covering.2| msc;

650 7 a| Combinatorics -- Graph theory -- Factorization, matching, partitioning, covering and packing.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Kühn, Daniela.?| UNAUTHORIZED;

700 1 a| Lo, Allan,d| 1983-?| UNAUTHORIZED;

700 1 a| Osthus, Deryk.?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30539167;

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The existence of designs via iterative absorption: hypergraph F-designs for arbitrary F / Stefan Glock, Daniela Kuhn, Allan Lo, Deryk Osthus.

Author/creator	Glock, Stefan
Other author	Kühn, Daniela.
Other author	Lo, Allan, 1983-
Other author	Osthus, Deryk.
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2023.
Description	v, 131 pages ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Block designs. Decomposition (Mathematics) Combinatorial packing and covering.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; Volume 284
Contents	Notation -- Outline of the methods -- Decompositions of supercomplexes -- Tools -- Nibbles, boosting and greedy covers -- Vortices -- Absorbers -- Proof of the main theorems -- Covering down -- Achieving divisibility -- Recent developments.
Abstract	"We solve the existence problem for F-designs for arbitrary r-uniform hypergraphs F. This implies that given any r-uniform hypergraph F, the trivially necessary divisibility conditions are sufficient to guarantee a decomposition of any sufficiently large complete r-uniform hypergraph into edge-disjoint copies of F, which answers a question asked e.g. by Keevash. The graph case r [equals] 2 was proved by Wilson in 1975 and forms one of the cornerstones of design theory. The case when F is complete corresponds to the existence of block designs, a problem going back to the 19th century, which was recently settled by Keevash. In particular, our argument provides a new proof of the existence of block designs, based on iterative absorption (which employs purely probabilistic and combinatorial methods). Our main result concerns decompositions of hypergraphs whose clique distribution fulfills certain regularity constraints. Our argument allows us to employ a 'regularity boosting' process which frequently enables us to satisfy these constraints even if the clique distribution of the original hypergraph does not satisfy them. This enables us to go significantly beyond the setting of quasirandom hypergraphs considered by Keevash. In particular, we obtain a resilience version and a decomposition result for hypergraphs of large minimum degree"-- Provided by publisher.
General note	"April 2023, Volume 284, Number 1406 (second of 6 numbers)"
Bibliography note	Includes bibliographical references (pages 129-131).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2023015045
ISBN	9781470460242 (paperback)
ISBN	(pdf)

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The existence of designs via iterative absorption: hypergraph F-designs for arbitrary F / Stefan Glock, Daniela Kuhn, Allan Lo, Deryk Osthus.

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