FoataMajorToInversions
Foata's bijection: each letter is put on the end of the image so far, which is cut into blocks, and every block is rotated one place right.
FoataMajorToInversions(Permutation)Foata's bijection: each letter is put on the end of the image so far, which is cut into blocks, and every block is rotated one place right.Typed signatures
| Type | Package | Applies |
|---|---|---|
((binary_word) -> binary_word) & ((composition) -> composition) & ((permutation) -> permutation) | combinatorics | always |
Details
- Takes a
Permutationand returns aPermutation— a typed map, so a wrong carrier is a type error rather than a wrong answer. - FindStat's Mp00067, Sage's foata_bijection. It sends the major index to the number of inversions; the inverse is FoataInversionsToMajor. Not the cycle-based Foata, which is FindStat's first fundamental transformation.
- Also takes a
IntegerComposition, returning aIntegerComposition: Foata's bijection on the word of parts: each part is put on the end of the image so far, which is cut into blocks, and every block is rotated one place right. - FindStat's Mp00314. An equal part counts as the smaller; it sends the major index to the number of inversions.
- Also takes a
BinaryWord, returning aBinaryWord: Foata's bijection on words: each letter is put on the end of the image so far, which is cut into blocks, and every block is rotated one place right. - FindStat's Mp00096. With repeated letters an equal letter counts as the smaller, so it is the permutation map through standardization; it sends the major index to the number of inversions.
Examples
About
| Examples | 3 |
|---|---|
| Crosswalk | FindStat ×3 |