Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
9 problems
Assuming that a minimal partition extender exists, is it unique?
If Δ is a simplicial complex such that depth k[Δ] ≥ dim k[Δ]-1 for all fields k , then Δ has a shelling extender.
What are the homotopy types of Q_n(Π) ? (in general their order complexes aren't necessarily spheres, or even Cohen-Macaulay)
Does a Nim-basis, if it exists, necessarily consist of the disjoint unions of circuits of the complex?
Let Δ be a Nim-regular complex, F a nonempty face, D_i a minimal cover of F by circuits and D = uplus_i D_i. Is it necessarily true that D - F is not a DUOC?
Give a bound R depending on some invariants of the simplicial complex Δ such that for r ≥R the polynomial h^sd^r(Δ)(t) has only real roots.
The magnitude homology of a graph obtained by gluing two cycle graphs C_3 along single edges to a single cycle graph C_4 has diagonal magnitude homology provided those triangles are not attached to opposite sides of the 4-cycle.
Can occurrences of mesh patterns be used to compute the Betti numbers of permutation complexes? Or can we define a set of mesh patterns P such that if π avoids P its permutation complex is contractible?
For central arrangements whose underlying matroid is connected, the homotopy type of the complement determines the underlying matroid.