InverseGlaisherFranklin

The inverse of GlaisherFranklin: repeated parts merge into doubled parts, and a leftover part splits into copies of its odd part.

FindStatMp00313via IntegerPartition↗

InverseGlaisherFranklin(IntegerPartition)The inverse of GlaisherFranklin: repeated parts merge into doubled parts, and a leftover part splits into copies of its odd part.

Typed signatures

Type	Package	Applies
(integer_partition) -> integer_partition	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a IntegerPartition and returns a IntegerPartition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00313. It sends the number of distinct repeated part sizes to the number of distinct even part sizes.

Examples

Basic #

the partition $4 + 2 + 1$

live ↗

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

About

Examples	1
Crosswalk	FindStat