OFFSET
0,3
COMMENTS
A set-system is a finite set of finite nonempty sets. The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. A weak antichain is a multiset of sets, none of which is a proper subset of any other.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(6) = 17 multiset partitions:
{1} {12} {123} {1234} {12345} {123456}
{1}{2} {1}{23} {1}{234} {1}{2345} {1}{23456}
{1}{2}{3} {12}{34} {12}{345} {12}{3456}
{1}{2}{12} {1}{2}{345} {123}{456}
{1}{2}{34} {1}{23}{45} {12}{13}{23}
{1}{2}{3}{4} {1}{2}{3}{23} {1}{23}{123}
{1}{2}{3}{45} {1}{2}{3456}
{1}{2}{3}{4}{5} {1}{23}{456}
{12}{34}{56}
{1}{2}{13}{23}
{1}{2}{3}{123}
{1}{2}{3}{456}
{1}{2}{34}{56}
{3}{4}{12}{34}
{1}{2}{3}{4}{34}
{1}{2}{3}{4}{56}
{1}{2}{3}{4}{5}{6}
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 15 2019
STATUS
approved