## Thursday, July 11, 2013

### On multiplicative lower sets

The set of all orders of elements of the symmetric group S_n forms a multiplicative lower set:
(#{0}
#{1}
#{2}
#{2 3}
#{3 4}
#{4 5 6}
#{4 5 6}
#{7 10 12}
#{7 8 10 12 15}
#{8 9 12 14 15 20})

The set of lower sets over the divisibility relation forms a distributive lattice with its own union and intersection operations.