9 problems

Let $M$ and $N$ be finitary matroids on a common ground set. For a set $I$, write $M/I$ and $N/I$ for the matroid contractions, and let $r(M/I)$ and $r(N/I)$ denote their ranks. An…

Nash-Williams' Matroid Intersection Conjecture. The matroids $M$ and $N$ admit a common independent set $I$ for which there is a partition

Let $E$ be a ground set, let $\mathfrak{F}(E)$ denote the relevant class of matroids on $E$, and for $j\in\{0,1\}$ let $\mathcal{I}_{M_j}$ be the collection of independent sets of…

Complementarity conditions conjecture. There always exist an $(I,t)$-linkage $\mathcal{P}$ and a vertex set $X\ni t$ such that $\mathcal{P}$ and $X$ satisfy the complementarity con…

Let $M$ and $N$ be tame matroids on the same ground set $E$. A packing for a pair of matroids on a set is a pair of disjoint spanning sets, one for each matroid, and a covering is…

Let $(D,B_0)$ be a dimaze, and let $M_L(D,B_0)$ be its linkability system. For every $I\in M_L(D,B_0)$ and every $B\subseteq B_0$, suppose there is a maximal independent set in…

Let $(M_k\mid k\in K)$ be a family of matroids on the same ground set $E$. A covering for $(M_k.Y\mid k\in K)$ is a family of independent sets whose union covers $Y$, and a packing…

Let $(M_k\mid k\in K)$ be a family of matroids. A wave is a set together with disjoint spanning sets for the restrictions of the matroids to that set; a family is unhindered when i…

Let $(M_k\mid k\in K)$ be a family of matroids on the same ground set $E$. A packing consists of pairwise disjoint spanning sets, one for each $M_k$, and a covering consists of ind…