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A generalization of Kneser ’ s Addition Theorem
| Content Provider | Semantic Scholar |
|---|---|
| Author | DeVos, Matt Goddyn, Luis A. Mohar, Bojan |
| Copyright Year | 2006 |
| Abstract | Let A = (A1, . . . , Am) be a sequence of finite subsets from an additive abelian group G. Let Σ`(A) denote the set of all group elements representable as a sum of ` elements from distinct members of A, and set H = stab(Σ`(A)) = {g ∈ G : g+Σ`(A) = Σ`(A)}. Our main theorem is the following lower bound: |Σ(A)| ≥ |H| ( 1− ` + ∑ Q∈G/H min { `,#{1 ≤ i ≤ m : Ai ∩Q 6= ∅} }) . In the special case when m = ` = 2, this is equivalent to Kneser’s addition theorem, and indeed we obtain a new proof of this result. The special case when every Ai has size one is a new result concerning subsequence sums which extends some recent work of Bollobás-Leader, Hamidoune, Hamidoune-Ordaz-Ortuño, and Grynkiewicz, and resolves a recent conjecture of Gao. ∗Supported by a Canada NSERC Discovery Grant †Supported in part by the Research Grant P1–0297 and by the CRC program. ‡On leave from: IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.fmf.uni-lj.si/~mohar/Reprints/2009/BM09_AM220_DeVos_KneserAdditionTh.pdf |
| Alternate Webpage(s) | http://www.sfu.ca/~mdevos/papers/capital.pdf |
| Alternate Webpage(s) | http://www.imfm.si/preprinti/PDF/01032.pdf |
| Alternate Webpage(s) | http://www.sfu.ca/~mohar/Reprints/2009/BM09_AM220_DeVos_KneserAdditionTh.pdf |
| Alternate Webpage(s) | http://people.math.sfu.ca/~goddyn/Papers/0711-capital-knesser.pdf |
| Alternate Webpage(s) | http://www.math.sfu.ca/~goddyn/Papers/0711-capital-knesser.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Bollobás–Riordan polynomial Cyclic redundancy check Familial Mediterranean Fever Generalization (Psychology) Maxima and minima Utility functions on indivisible goods |
| Content Type | Text |
| Resource Type | Article |
