CyclicShift from ParkingFunction

Rotate the word one place to the left: the first entry moves to the end.

ParkingFunction → ParkingFunctioninverse

Called as CombinatorialMap(x, "CyclicShift"). The head's page has its examples.

Live

Explore

Each element of ParkingFunction at a size, and its image, applied in your browser; sizes past 6 are not offered.

Size

Properties

Sizes 1 to

Transport a statistic

Pick a statistic on ParkingFunction. Its distribution over the images of ParkingFunction at each size is computed, and compared with the 9 statistics on ParkingFunction: those that share it are the ones the map sends it to, as far as the sizes computed show.

Statistic LuckyCarsTotalParkingDisplacementMaximalParkingDisplacementSumLessLengthCriticalLeftToRightMaximaDeficienciesInitialIncreasingSegmentLengthTiesCenterSize Sizes 1 to

Also from

The same name out of other carriers, each its own implementation: Permutation, SetComposition, IntegerComposition, BinaryWord.

FindStat Mp00293

rotate front-to-back

Matched by value: our map agrees with FindStat's image on each of the 1200 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

BijectionGraded mapas FindStat records them, checked by FindStat's contributors.

Rotate a parking function by moving the first entry to the last position.

Object	Image
[1]	[1]
[1,1]	[1,1]
[1,2]	[2,1]
[2,1]	[1,2]

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00293 has the rest.