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- W1999531807 abstract "When every set in a setpartition Open image in new window has size one, the DeVos-Goddyn-Mohar (DGM) Theorem gives a lower bound for |Σ n (S)|, where Open image in new window is the sequence partitioned by the setpartition Open image in new window . As seen in previous exercises, this is really a lower bound for Open image in new window , where the union runs over all n-setpartitions Open image in new window with Open image in new window . In other words, the DGM theorem, in this special case, gives a lower bound for the size of the union of all sumsets of the n-setpartitions of S. In this chapter, we present two versions of a sibling result to the DGM Theorem. Both essentially give the existence of a single n-setpartition Open image in new window with large sumset. The first is stronger in statement and generalizes the aforementioned case of the DGM Theorem. The second is weaker in statement, but also valid in the much more general context of homomorphism weighted subsequence sums." @default.
- W1999531807 created "2016-06-24" @default.
- W1999531807 creator A5040241644 @default.
- W1999531807 date "2013-01-01" @default.
- W1999531807 modified "2023-09-27" @default.
- W1999531807 title "The Partition Theorem II" @default.
- W1999531807 cites W1996963858 @default.
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- W1999531807 doi "https://doi.org/10.1007/978-3-319-00416-7_15" @default.
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