4 problems

Generalized connectivity conjecture. There exists a function $f: \mathbb{N}^2 \rightarrow \mathbb{N}$ such that if $M$ has no circuits of size at most $2s-1$, no cocircuits of size…

Brettell–Chun–Goddyn–Whittle conjecture. There exists a function $f: \mathbb{N} \rightarrow \mathbb{N}$ such that if $M$ is a $(2t-1)$-connected matroid with no circuits or cocircu…

Chain theorem conjecture. There exists a function $f(t)$ such that if $M$ is a $(2t-1)$-connected matroid with no circuits or cocircuits of size $2t-1$ and

Generalised spike-structure conjecture. There exists a function $f(t_1,t_2)$ such that if $M$ is a matroid with the $(t_1,2t_1,t_2,2t_2)$-property and