# Statistics on partitions equidistributed with number of even parts

Fix a positive integer $n$. For a partition $λ$ of $n$, let $e(λ)$ be the number of even parts in $λ$. Using bijections, we can show the statistic $e(λ)$ is equidistributed on the set of partitions of $n$ with the following statistics:

(1) The largest part in $λ$ that occurs more than once.

(2) $∑⌊a_i/2⌋$, where $a_i$ is the number of occurrences of $i$ in $λ$.

(3) The number of cells in the Young diagram of $λ$ whose leg is zero and arm is odd.

Question: are there any other statistics equidistributed with $e(λ)$ that admit bijective descriptions?

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We have none of these statistics so far in the FindStat project at findstat.org. Would you be willing to add those, together with a brief description or reference why they are interesting? –  Christian Stump Jun 24 '13 at 5:38
I agree with Christian, put the thing in FindStat! –  Per Alexandersson Jun 24 '13 at 14:02