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Seb Destercke
Seb Destercke
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Maximal number of antichains of a strongly connected poset

Assume we have a strongly connected poset $P$ of $n$ elements, I am searching to know what is the maximal number of antichains such a poset can have?

$2^n$ is obviously an upper bound, and my feeling is that the maximal number is actually $2^{n-1}$, however I could find the answer in related questions (nor after a quick look at related literature).

Maximal number of antichains of a strongly connected poset

Assume we have a strongly connected poset of $n$ elements, I am searching to know what is the maximal number of antichains such a poset can have?

$2^n$ is obviously an upper bound, and my feeling is that the maximal number is actually $2^{n-1}$, however I could find the answer in related questions (nor after a quick look at related literature).

Maximal number of antichains of a connected poset

Assume we have a connected poset $P$ of $n$ elements, I am searching to know what is the maximal number of antichains such a poset can have?

$2^n$ is obviously an upper bound, and my feeling is that the maximal number is actually $2^{n-1}$, however I could find the answer in related questions (nor after a quick look at related literature).

Source Link
Seb Destercke
Seb Destercke
  • 123
  • 3

Maximal number of antichains of a strongly connected poset

Assume we have a strongly connected poset of $n$ elements, I am searching to know what is the maximal number of antichains such a poset can have?

$2^n$ is obviously an upper bound, and my feeling is that the maximal number is actually $2^{n-1}$, however I could find the answer in related questions (nor after a quick look at related literature).