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This question is crossposted from math.stackexchange.com, where it remains unanswered. Let $Y$ be a Young tableau of shape $\lambda:=(\lambda_1,\ldots,\lambda_n)$, where $\lambda_1\geq\lambda_2\geq\l …

The usual branching rule says that $$f_\lambda=\sum_{\mu\rightarrow\lambda}f_\mu,$$ where the sum is taken over all partitions $\mu$ of $n-1$ that are contained ($\rightarrow$) in $\lambda$. …

The only similar types of tableaux that I've seen are called composition tableaux (mainly because they allow for non-monotonically decreasing partitions), which come up in definitions of quasisymmetric …

Let $T_{\lambda}$ be the set of standard young tableaux (SYT) of shape $\lambda_1\geq \lambda_2\cdots\geq \lambda_n$. Now consider pushing a row $\mu$ with $\mu\geq \lambda_1$ onto $Y$ to give shape $ …

Restricting the above sequence to length $n$ to give the Plancheral measure on partitions of $n$. …

First, is there an obvious restriction on $f$ to give $k$-bounded weak reverse partitions? … In both of these equations, I fail to see how one would obtain a uniform measure on the all such partitions. …