Paradoxical Decompositions of the Cube and Injectivity
β Scribed by Wright, J. D. M.
- Book ID
- 120092690
- Publisher
- Oxford University Press
- Year
- 1990
- Tongue
- English
- Weight
- 162 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0024-6093
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## Abstract We prove that if T is any tree having __n__ edges (__n__ β₯ 1), then the __n__βcube Q~n~ can be decomposed into 2^nβ1^ edgeβdisjoint induced subgraphs, each of which is isomorphic to T. We use this statement to obtain two results concerning decompositions of Q~n~ into subgraphs isomorphi
## dedicated to rΓΌdiger gΓΆbel on the occasion of his 60th birthday We give a criterion for the existence of an indecomposable decomposition of pure-injective objects in a locally finitely presented Grothendieck category (Theorem 2.5). As a consequence we get Theorem 3.2, asserting that an associat