InternalPoints

Elements with an earlier and a later element whose blocks open after theirs does.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000562via SetPartition✓↗

InternalPoints(partition)Elements with an earlier and a later element whose blocks open after theirs does.

Typed signatures

Type	Package	Applies
(set_partition) -> number	combinatorics	always

Domain: Set partition statistics

Details

• Defined over SetPartition as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a SetPartition and nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer.
• An element e is internal when some f < e < g have blocks with larger least element than e's block (Mansour, Section 5.5).

Examples

Basic #

the partition $\{1,3\} \mid \{2\}$

live ↗

In$\mathrm{InternalPoints}({\operatorname{SetPartition}}([[1, 3], [2]]))$Out$0$

the partition $\{1\} \mid \{2,4\} \mid \{3\}$

live ↗

In$\mathrm{InternalPoints}({\operatorname{SetPartition}}([[1], [2, 4], [3]]))$Out$0$

Properties #

FindStat's value for {{1,2}}

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{SetPartition}}([[1, 2]]), \text{InternalPoints})$Out$0$

Known value · FindStat St000562

FindStat's value for {{1,2,3}}

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{SetPartition}}([[1, 2, 3]]), \text{InternalPoints})$Out$0$

Known value · FindStat St000562

FindStat's value for {{1},{2}}

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{SetPartition}}([[1], [2]]), \text{InternalPoints})$Out$0$

Known value · FindStat St000562

About

Examples	5
Crosswalk	FindStat