I am looking for the name of the following map $t(\mu)$, defined for integer partitions $\mu=\mu_1\geq\mu_2\geq\dots$:

  1. if $\mu$ is empty, return $\mu$.
  2. if the first part $\mu_1$ of $\mu$ is at least the number of parts of $\mu$, return the partition $\mu_1, t(\mu_2,\dots)$
  3. otherwise, let $\lambda=\mu^t$ and return $\lambda_1, t(\lambda_2,\dots)$.

One property of $t$ is that $t(\mu)$ dominates $\mu$, but I'm not sure whether this is the maps natural context.


The partitions produced by the map are called superdiagonal partitions in OEIS, so absent a better reference you could call it the superdiagonalising map.

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  • $\begingroup$ SSSSSSSSSSuper! $\endgroup$ – Martin Rubey Apr 20 '17 at 15:44
  • $\begingroup$ Or, depending on your British/American English preference, superdiagonalizing. $\endgroup$ – Brian Hopkins Apr 20 '17 at 16:43

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