ExponensConsonantiae

The least common multiple of the parts over their greatest common divisor.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001128via IntegerPartition✓↗

ExponensConsonantiae(partition)The least common multiple of the parts over their greatest common divisor.

Typed signatures

Type	Package	Applies
(integer_partition) -> number	combinatorics	always

Domain: Partition statistics

Details

• Defined over IntegerPartition as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a IntegerPartition 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 IntegerPartition, over _x

0 if Length(_x) < 1 else Fold(Function(LCM(a, b), a, b), _x[1], Rest(_x)) / Fold(
                                                                                  Function(a * b /
                                                                                           LCM(a, b), a, b),
                                                                                  _x[1],
                                                                                  Rest(_x),
                                                                                )

Examples

Basic #

the partition $4 + 2 + 1$ of $7$

live ↗

In$\mathrm{ExponensConsonantiae}({\operatorname{IntegerPartition}}([4, 2, 1]))$Out$4$

the partition $3 + 3 + 1$ of $7$

live ↗

In$\mathrm{ExponensConsonantiae}({\operatorname{IntegerPartition}}([3, 3, 1]))$Out$3$

Properties #

FindStat's value for [2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([2]), \text{ExponensConsonantiae})$Out$1$

Known value · FindStat St001128

FindStat's value for [3]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([3]), \text{ExponensConsonantiae})$Out$1$

Known value · FindStat St001128

FindStat's value for [4]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([4]), \text{ExponensConsonantiae})$Out$1$

Known value · FindStat St001128

About

Examples	5
Crosswalk	FindStat