4 problems

For every finite simple connected graph $G$ containing a cycle, define $t(G)=\max\{|S|:S\subseteq V(G)\text{ and }G[S]\text{ is a tree}\}$, let $g(G)$ be the length of a shortest c…

For every finite simple connected graph $G=(V,E)$, let $N_G(v)$ denote the neighborhood of $v$, let $\alpha(G[N_G(v)])$ be the independence number of the subgraph induced by…

For $N=2^n$, let $s\in\mathbb{Z}_N$ be hidden. Given polynomially many independent copies of the mixed coset state…

Conjecture 9.1 proposes the identity … where $\mathsf{LD}(0,n)^{\ast k,\circ r}$ is the set of positively labelled Dyck paths of size $n$ with $k$ decorated rises and $r$ decorated…