BinaryWord from Finset

A subset of 1..n as its characteristic word: letter i is 1 when i is a member.

Finset → BinaryWordinverse

Not order-preserving: Subsets lists subsets by size, then lex, while BinaryWords(n) through Finset(word) gives them in their characteristic words' order.

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

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Each element of Finset at a size, and its image, applied in your browser; sizes past 7 are not offered.

Size

Properties

Sizes 1 to

Transport a statistic

Pick a statistic on BinaryWord. Its distribution over the images of Finset at each size is computed, and compared with the 0 statistics on Finset: those that share it are the ones the map sends it to, as far as the sizes computed show.

Statistic HammingWeightLeadingOnesCountOnePositionSumOneRunCountOddOneRunCountLongestRunOfOnesChangeCountPathDepthOnesMinusZerosBalancedPrefixCountSymmetryDegreeAscentsInversionsMajorIndexLongestConstantRunLongestAlternatingFactorFirstOnePositionAfterAppendedOneDecimalRepresentationDecimalRepresentationWithLeadingOneDistinctFactorCountBorderLengthSymmetricBorderLengthInversionSumNonInversionSumStrictlyIncreasingRunsMinimalPeriodBorderCountWeakMajorIndexDistinctSubsequenceCountRepetitionExponentBalanceShortestPalindromicDecompositionLengthPalindromicDecompositionCountLongestCatalanFactorSemilengthCatalanFactorCountCriticalStepCountInternalInversionsUniqueFactorLengthLyndonFactorizationLengthLongestYamanouchiPrefixLongestPalindromicPrefixLongestPalindromicFactorLongestPalindromicSubsequenceDistinctCubeCountDistinctSquareCountCyclicShiftIndexDescentWordPreimageCountLatticePathsAboveWordCountSameEndpointPathsAboveWordCountEvenPalindromicPrefixHalfLengthOddPalindromicPrefixHalfLengthLongestPalindromicFactorStartingWithOneReverseComplementFactorHalfLengthReverseComplementFactorHalfLengthStartingWithOneFlexModularMajorIndexValleyFillingDegreeBaselineCrossingsPrimitiveFactorCount Sizes 1 to

Also from

The same name out of other carriers, each its own implementation: DyckPath, IntegerPartition.