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Instant-use add-on functions for the Wolfram Language
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Compute the pseudo-conjugate of an integer partition
ResourceFunction["PseudoConjugatePartition"][x] gives the pseudo-conjugate partition of the integer partition x. |
Compute the pseudo-conjugate of an integer partition:
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The partition rank of a partition and its conjugate have opposite signs:
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Similarly, the partition crank of a partition and its pseudo-conjugate have opposite signs:
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Remarkably, the self-conjugate partitions and the self-pseudo-conjugate partitions of n are equinumerous; here n=23:
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Compute the total number of self-pseudo-conjugate partitions of n from the generating function:
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Compare with a brute-force enumeration:
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Wolfram Language 12.3 (May 2021) or above
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