NegateSigns from SignedPermutation

Every sign reversed: multiplication by the longest element −id of the hyperoctahedral group.

SignedPermutation → SignedPermutationbijectioninvolution

FindStat's Mp00244, "bar".

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

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Each element of SignedPermutation 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 SignedPermutation. Its distribution over the images of SignedPermutation at each size is computed, and compared with the 18 statistics on SignedPermutation: those that share it are the ones the map sends it to, as far as the sizes computed show.

Statistic NegativeEntryCountPositiveEntryCountTypeBInversionCountNegativeSumPairCountFlagMajorIndexFlagDescentFlagExcedanceFlagWeakExcedancePositiveBeforeLargerNegativePairCountIncreasingPositivePairCountPositiveBeforeNegativeCountRightDescentsSignedPermutationOrderSignedReflectionLengthFlagDenertIndexSignedSortingIndexSignedAlignmentCountStasinskiVollLength Sizes 1 to

FindStat Mp00244

bar

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 mapInvolutionas FindStat records them, checked by FindStat's contributors.

Return the signed permutation with all signs reversed.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00244 has the rest.