Conjugate Partition
ConjugatePartitions
Pairs of partitions for a single number whose Ferrers diagrams transform into each other when reflected about the line y=-x, with the coordinates of the upper left dot taken as (0, 0), are called conjugate (or transpose) partitions. For example, the conjugate partitions illustrated above correspond to the partitions 6+3+3+2+1 and 5+4+3+1+1+1 of 15. A partition that is conjugate to itself is said to be a self-conjugate partition.
The conjugate partition of a given partition p is implemented in the Wolfram Function Repository as ResourceFunction["ConjugatePartition"][p].
See also
Durfee Square, Ferrers Diagram, Partition Function P, Self-Conjugate PartitionExplore with Wolfram|Alpha
WolframAlpha
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References
Andrews, G. E. The Theory of Partitions. Cambridge, England: Cambridge University Press, pp. 7-8, 1998.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 55-56, 1990.Referenced on Wolfram|Alpha
Conjugate PartitionCite this as:
Weisstein, Eric W. "Conjugate Partition." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ConjugatePartition.html