6 problems

Let $\lambda$ and $\mu$ be partitions with $\mu\subseteq\lambda$, and let $\lambda/\mu$ be the resulting skew partition. Its rank, denoted ${\rm rank}(\lambda/\mu)$, is the smalles…

Bounded-height skew-tableaux asymptotic conjecture. There is a constant $C_d>0$, depending only on $d$, such that

Let $\mu\subseteq\lambda$ be partitions, let $\ell$ be the length of $\lambda$, and fix an integer $n\geq\ell$. Let $H_{\lambda/\mu}(n;q)$ be the skew $q$-hook-content quantity and…

Let $\mu\subseteq\lambda$ be partitions, and let $f^{\lambda/\mu}_q$ be the skew $q$-hook-length quantity. Assume it can be written as a rational function … where…

Let $\overline{H}_{\lambda/\mu}(n)$ be the normalized hook-content quantity associated with partitions $\mu\subseteq\lambda$, and let $\ell$ denote the length of $\lambda$. For an…

A graph is Berge if it has no odd hole and no odd antihole. A balanced skew partition is the balanced form of a skew partition used in the decomposition theory of Berge graphs. A g…