3 problems

Let $\operatorname{\mathcal{T}}_{4,n}$ be the set of interlacing triangular arrays of rank $4$ and height $n$, and let $\square_n$ be the $n\times n$ square grid graph. An edge lab…

Let $\operatorname{\mathcal{T}}_{4,n}$ denote the set of interlacing triangular arrays of rank $4$ and height $n$. Let $\square_n$ be the $n\times n$ square grid graph, and let…

Let $[m]=\{1,\ldots,m\}$. For integers $m,n\geq 1$ and tuples $\lambda^{(i)}\in[m]^n$ for $i=1,\ldots,m$, let $\operatorname{\mathcal{T}}_{m,n}(\lambda^{(1)},\ldots,\lambda^{(m)})$…