A327438 Irregular triangle read by rows with trailing zeros removed where T(n,k) is the number of unlabeled antichains of nonempty subsets of {1..n} with spanning edge-connectivity k.

1, 1, 1, 3, 1, 6, 2, 1, 15, 7, 5, 2, 52, 53, 62, 31, 9, 1, 1

Offset: 0

Author

Gus Wiseman, Sep 11 2019

Keywords

• nonn
• tabf
• more

Comments

An antichain is a set of sets, none of which is a subset of any other.

The spanning edge-connectivity of a set-system is the minimum number of edges that must be removed (without removing incident vertices) to obtain a set-system that is disconnected or covers fewer vertices.

Examples

			Triangle begins:
   1
   1  1
   3  1
   6  2  1
  15  7  5  2
  52 53 62 31  9  1  1
The antichains counted in row n = 4 are the following:
  0             {1234}         {12}{134}{234}     {123}{124}{134}{234}
  {1}           {12}{134}      {123}{124}{134}    {12}{13}{14}{23}{24}{34}
  {12}          {123}{124}     {12}{13}{24}{34}
  {123}         {12}{13}{14}   {12}{13}{14}{234}
  {1}{2}        {12}{13}{24}   {12}{13}{14}{23}{24}
  {1}{23}       {12}{13}{234}
  {12}{13}      {12}{13}{14}{23}
  {1}{234}
  {12}{34}
  {1}{2}{3}
  {1}{2}{34}
  {2}{13}{14}
  {12}{13}{23}
  {1}{2}{3}{4}
  {4}{12}{13}{23}
		

Crossrefs

Row sums are A306505.

Column k = 0 is A327437.

The labeled version is A327352.

Cf. A014466, A052446, A327062, A327071, A327103, A327111, A327144, A327352, A327353.