Rowmotion

Rowmotion of the word as an order ideal of a product of two chains: the stretches between valleys reversed, each valley written 10.

FindStatMp00278via BinaryWord↗Mp00281via SignedPermutation↗

Rowmotion(BinaryWord)Rowmotion of the word as an order ideal of a product of two chains: the stretches between valleys reversed, each valley written 10.

Typed signatures

Type	Package	Applies
((binary_word) -> binary_word) & ((signed_permutation) -> signed_permutation)	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a BinaryWord and returns a BinaryWord — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00278. A bijection that keeps the number of ones; its order is the length of the word.
• Also takes a SignedPermutation, returning a SignedPermutation: Rowmotion of the signed permutation with respect to the sorting order, through its signed Lehmer code.
• FindStat's Mp00281, a bijection. The sorting order is Armstrong's, for the Coxeter element −n, 1, …, n − 1.

Examples

Basic #

the binary word $01100$

live ↗

In$\mathrm{Rowmotion}({\operatorname{BinaryWord}}([0, 1, 1, 0, 0]))$Out${\operatorname{BinaryWord}}([1, 0, 0, 0, 1])$

the signed permutation $2\,\bar 3\,1$

live ↗

In$\mathrm{Rowmotion}({\operatorname{SignedPermutation}}([2, -3, 1]))$Out${\operatorname{SignedPermutation}}([3, 1, -2])$

About

Examples	2
Crosswalk	FindStat ×2