BlockSizeSpan

Largest block size minus smallest.

BlockSizeSpan(partition)Largest block size minus smallest.

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.

Definition

Epsil, as the implementation runs it.

on SetPartition, over _x

0 if Length(_x) < 1 else Max(Map(Function(Length(b), b), _x)) - Min(Map(
                                                                         Function(Length(b), b),
                                                                         _x,
                                                                       ))

Examples

Basic #

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

live ↗

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

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

live ↗

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

About

Examples	2