13 problems

Let $[sigma,pi]$ be an interval of the classical permutation pattern poset. A subinterval is a zero split subinterval if it has the zero-split property described for this poset. Sh…

Let … -complex, with vertex set the pinched braids having precisely one regular strand. Sphericality conjecture. … is large enough. The paper presents this as evidence toward under…

Reiner's conjecture. If $[I,J]$ is facial, then it is spherical. If $[I,J]$ is not facial, then it is contractible.

Wedge-of-spheres conjecture.

Irreducible-support stability conjecture. For $t\geqslant3$, every irreducible appearing in $\tilde{H}_{n-2}(B_n^{(t)})$ also appears in $\tilde{H}_{n-2}(B_n^{(2)})$.

Equivariant inclusion conjecture. For $t\geqslant1$, there are $\mathfrak{S}_n$-equivariant inclusions

Top elementary coefficient conjecture. The coefficient of $e_n$ is always $1$, that is, $a_{(n)}=1$.

Let $\Lambda$ be a finite-dimensional algebra, and let $\tau\text{-}\mathsf{perp}(\mathsf{mod}\Lambda)$ denote the poset of $\tau$-perpendicular subcategories of…

Let $A$ be an alphabet of size $n\ge 2$, and let $S_n$ act on $A^*$ by permuting the alphabet. A rank-selected subposet is obtained by retaining words whose ranks belong to a finit…

Let $A$ be an alphabet of size $n\ge 2$, and let $S_n$ act on $A^*$ by permuting the alphabet. A rank-selected subposet is obtained by retaining words whose ranks belong to a finit…

Let $B(n,d)$ be the higher Bruhat order, and let an interval of $B(n,d)$ be facial if it arises from the set of simple arrangements obtained by resolving the crossings of a non-sim…

Let $B_n$ be the Boolean algebra of subsets of an $n$-element set, and let $B_n\setminus\{\emptyset\}$ be its truncation with the minimum element removed. Let $C_{n-1}$ be a chain…

Let $G$ be a finite solvable group, and let $L(G)$ denote its subgroup lattice. Choose a chief series … A complement to a subgroup $N$ is a subgroup $H$ with $HN=G$ and $H\cap N=1$…