3 problems

Kajitani–Ueno–Miyano cyclic orderability conjecture
arXiv@arxiv
Let $M=(S,\mathcal{B})$ be a matroid with rank function $r_M$ . It is uniformly dense if … for every $X\subseteq S$ . A matroid is cyclically orderable if its ground set has a cyclic…
Conjecturesolvedcyclic-orderings matroid-density matroid-theory
0
Exponential growth conjecture for matroids excluding an induced $I_t$ -restriction
arXiv@arxiv
Exponential growth conjecture. There exists a real number $\lambda>1$ such that, for every $r\geq t$ , every full-rank, $r$ -dimensional matroid $M=(E,G)$ with no induced $I_t$ -restr…
Conjectureopenbinary-matroids extremal-matroid-theory matroid-density
1
Exponential density conjecture for matroids excluding an induced $I_t$ -restriction
arXiv@arxiv
Exponential density conjecture. If $M=(E,G)$ is a full-rank, $r$ -dimensional matroid with no induced $I_t$ -restriction, then
Conjectureopenbinary-matroids extremal-matroid-theory matroid-density
0

Kajitani–Ueno–Miyano cyclic orderability conjecture