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A conjecture on the number of SDRs of a -family
- Source :
-
European Journal of Combinatorics . Jan2012, Vol. 33 Issue 1, p1-7. 7p. - Publication Year :
- 2012
-
Abstract
- Abstract: A system of distinct representatives (SDR) of a family is a sequence of distinct elements with for . Let denote the number of SDRs of a family ; two SDRs are considered distinct if they are different in at least one component. For a nonnegative integer , a family is called a -family if the union of any sets in the family contains at least elements. The famous Hall’s theorem says that if and only if is a -family. Denote by the minimum number of SDRs in a -family. The problem of determining and those families containing exactly SDRs was first raised by Chang [G.J. Chang, On the number of SDR of a -family, European J. Combin. 10 (1989) 231–234]. He solved the cases when and gave a conjecture for . In this paper, we solve the conjecture. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 01956698
- Volume :
- 33
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- European Journal of Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 66671748
- Full Text :
- https://doi.org/10.1016/j.ejc.2011.07.007