9 problems

A matroid is subsequence-interchangeably base orderable (SIBO) if every pair of bases admits the subsequence exchange orderings specified in the paper. Sparse-paving SIBO conjectur…

Let $M$ be a connected matroid of rank $r$ on $[n]$. Write $U_{r,n}$ for the uniform matroid of rank $r$ on $[n]$, let $d_\lambda(M)$ denote the Schubert coefficient indexed by a p…

For each positive integer $n$, let $\mathsf{S}_n$ be the sparse paving matroid on $[n]$ of rank $\lfloor n/2\rfloor$ with the maximal possible number of circuit-hyperplanes and lex…

Representability conjecture for K(r,t). Every matroid obtained from $K(r,t)$ by relaxing a circuit-hyperplane into a basis is representable.

For each positive integer $n$, let $\operatorname{mat}(n)$ and $\operatorname{mat}'(n)$ be the numbers of matroids on $[n]$, respectively counted with labels and up to isomorphism.…

A matroid is sparse paving if its nonspanning circuits are hyperplanes; equivalently, no nonbasis of size equal to the rank can be transformed into another nonbasis by exchanging o…

A matroid stack delta-matroid is a delta-matroid whose proper set systems in its stack are matroids. It is sparse paving when every matroid in its stack is sparse paving, meaning t…

Sparse paving minor conjecture for sparse paving matroids. Let $N$ be a fixed sparse paving matroid. Asymptotically almost every sparse paving matroid has an $N$-minor.

Sparse paving minor conjecture. Let $N$ be a fixed sparse paving matroid. Asymptotically almost every matroid has an $N$-minor.