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May 2, 2022 at 18:32 history edited T. Amdeberhan CC BY-SA 4.0
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May 2, 2022 at 17:58 comment added Sam Hopkins A nice combinatorial approach to (1) and (2) is via the dual graded graphs of Fomin (building on Stanley's differential posets). But I don't think this works to give something for partitions whose parts differ by $r$ for $r \geq 2$.
May 2, 2022 at 17:48 history asked T. Amdeberhan CC BY-SA 4.0