Records

The number of records (left-to-right maxima) of : positions with for all .

Records(p)the record count of a one-line permutation

Domain: Permutation statistics

Details

• The first position is always a record vacuously, so for
• Equidistributed with CycleCount over (Foata's bijection), so both follow the unsigned Stirling numbers of the first kind

Examples

See also: CycleCount, StirlingS1, SymmetricGroup