5 problems

Let $Q$ be a sorting and alternating word in a Coxeter group with longest element $\omega_\circ$, let $\mathsf{Brick}(Q,\omega_\circ)$ be the associated brick polytope, and let…

Graphical-zonotope facet deletion conjecture. Removing the appropriate inequalities from the facet description of $\Zono$ defines a realization of the quotient fan

Coherent quotient fan conjecture. The quotient fan of any coherent congruence of $\AR$ can be realized by deleting inequalities in the facet description of the graphical zonotope o…

Let the weak order on the symmetric group be quotiented by a lattice congruence, and represent its intervals by semi-crossing arc bidiagrams. An interval is inclusion minimal if it…

Let $W$ be the Coxeter group with simple generators $S$, let $\equiv$ be the lattice congruence under consideration, and let $xW_I$ be a coset of a standard parabolic subgroup. A c…