IncreasingCyclePermutation

The permutation whose cycles are the blocks, each cycle increasing: every element goes to the next larger in its block, the largest to the least.

FindStatMp00080via SetPartition↗

IncreasingCyclePermutation(SetPartition)The permutation whose cycles are the blocks, each cycle increasing: every element goes to the next larger in its block, the largest to the least.

Typed signatures

Type	Package	Applies
(set_partition) -> permutation	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a SetPartition and returns a Permutation — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00080, Sage's to_permutation. Injective; it maximizes the exceedances among the permutations with these cycles.

Examples

Basic #

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

live ↗

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

About

Examples	1
Crosswalk	FindStat