Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4646582 | Discrete Mathematics | 2016 | 12 Pages |
Abstract
If a group GG is the union of proper subgroups H1,…,HkH1,…,Hk, we say that the collection {H1,…,Hk}{H1,…,Hk} is a cover of GG, and the size of a minimal cover (supposing one exists) is the covering number of GG, denoted by σ(G)σ(G). Maróti showed that σ(Sn)=2n−1σ(Sn)=2n−1 for nn odd and sufficiently large, and he also gave asymptotic bounds for nn even. In this paper, we determine the exact value of σ(Sn)σ(Sn) when nn is divisible by six.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Eric Swartz,