3 problems

Let $T$ be a tree, let $t$ be a positive integer, and let $J_t(T)$ denote the $t$-connected ideal of $T$. Let $\operatorname{bight}(J_t(T))$ denote the big height of this ideal. Pr…

Let $T$ be a tree, let $t$ be a positive integer, and let $J_t(T)$ denote the $t$-connected ideal of $T$. Let $\mathcal H$ be the hypergraph corresponding to $J_t(T)$, and write…

Regularity conjecture for t-path ideals. The displayed formula should hold. In particular,