RunSort

The permutation with its increasing runs sorted lexicographically.

RunSort(Permutation)The permutation with its increasing runs sorted lexicographically.

Typed signatures

Type	Package	Applies
`((binary_word) -> binary_word) & ((permutation) -> permutation)`	`combinatorics`	always

Domain: Combinatorial maps

Details

Takes a Permutation and returns a Permutation — a typed map, so a wrong carrier is a type error rather than a wrong answer.
FindStat's Mp00223. Lossy: the runs' order is forgotten.
Also takes a BinaryWord, returning a BinaryWord: The word with its weakly increasing runs sorted lexicographically.
FindStat's Mp00224. Lossy: the runs' order is forgotten. The runs are the maximal stretches 0...01...1.

Examples

Basic #

the one-line word $231$

\mathrm{RunSort}({\operatorname{Permutation}}([2, 3, 1]))

Out

{\operatorname{Permutation}}([1, 2, 3])

the binary word $01100$

\mathrm{RunSort}({\operatorname{BinaryWord}}([0, 1, 1, 0, 0]))

Out

{\operatorname{BinaryWord}}([0, 0, 0, 1, 1])

About

Examples	2
Crosswalk	FindStat ×2