6 problems

Let $b=\frac{2}{\beta}-1$. The hypermap series enumerates bipartite maps with independently specified profiles of the two types of vertices, and its coefficients are denoted by…

Let $\pi$, $\mu$, and $\nu$ be partitions, and let $g^\pi_{\mu,\nu}$ denote the corresponding hypermap coefficient. Set $b:=\alpha-1$. Sniady's conjecture. For any partitions $\pi$…

Strong automorphism realisation conjecture. The condition that at least one of $p$, $q$ and $r$ is $\infty$ can be omitted from the countable and strong automorphism realisation as…

Fix a positive integer $a$. Let $M_{g,n}^{[a]}(b_1,\ldots,b_n)$ be the enumeration numbers of $a$-hypermaps. A function is a quasi-polynomial modulo $a$ if its polynomial expressio…

For a positive integer $a$, let $M_{g,n}^{[a]}(b_1,\ldots,b_n)$ denote the enumeration coefficients of $a$-hypermaps, and let $\omega_{g,n}$ be the correlation differentials produc…

Let $m$ and $n$ be positive integers satisfying … Singerman's conjecture. There is an orientably regular chiral map of type $\{m,n\}$. This conjecture predicts the existence of chi…