7 problems

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…

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 $\tilde{H}_{n-2}(B_n^{(2)})$.

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

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 $G$ 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 $H\cap N=1$…