On the covering number of symmetric groups having degree divisible by six

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.