GlaisherFranklin

The Glaisher-Franklin bijection: even part sizes halved become repeated parts, and repeated odd parts merge into their binary multiples.

FindStatMp00312via IntegerPartition↗

GlaisherFranklin(IntegerPartition)The Glaisher-Franklin bijection: even part sizes halved become repeated parts, and repeated odd parts merge into their binary multiples.

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 Mp00312. It sends the set of even part sizes, each halved, to the set of repeated part sizes.

Examples

Basic #

the partition $4 + 2 + 1$

live ↗

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

About

Examples	1
Crosswalk	FindStat