3 problems

Let $n$ be the number of pairs of matrix entries in the Weingarten function and let $N$ be the matrix size. The large-$N$ limit is said to hold uniformly when $n$ grows with $N$ wi…

Let $W\!g(\sigma)$ denote the Weingarten function, and write its expansion in terms of coefficients $c_\lambda$ indexed by partitions $\lambda$ of the relevant degree, with partiti…

Let $P_n(d)$ be the polynomial defined by the orthogonal Weingarten-function formula in the preceding discussion, for a positive integer $n$. Coefficient nonnegativity conjecture.…