Function Repository Resource:

PermutationIndex

Give the lexicographic index of a permutation

Contributed by: Ed Pegg Jr

ResourceFunction["PermutationIndex"][perm]

gives the lexicographic index of permutation perm.

Details and Options

Permutations are considered to be in normal sorted order.

Lehmer codes are generated as an intermediary step.

The generating algorithm for Lehmer codes is as follows: For each number in the permutation, count how many subsequent values it exceeds.

Return the index of a permutation:

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The first permutation of a given length has index 1:

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Some large permutations:

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Large permutations can be indexed:

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Terms don’t necessarily need to be positive or integer:

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The indices of permutations and negative permutations are balanced:

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Differences of indices of even permutations:

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