11 problems

Let $m\in\mathbb{P}$, and let $c(\operatorname{\mathcal{W}}(B_{2m}))$ be the convex hull of the signed Wachs permutations in $\mathbb{R}^{2m}$. Simplicity conjecture. The polytope…

Let $n\in\mathbb{P}$, and let $\mu(u,v)$ denote the Möbius function of the Bruhat-order interval $[u,v]$ in the poset of signed Wachs permutations $\operatorname{\mathcal{W}}(B_n)$…

Smooth Schubert enumeration conjecture. The number of signed permutations in $S_n^B$ that simultaneously index smooth Schubert varieties in types B and C is equal to the number of…

Grassmannian and bigrassmannian avoidance conjecture. A signed permutation is Grassmannian if and only if it globally avoids every pattern in $P$, and it is bigrassmannian if and o…

Let $T(n,k)$ be the sequence defined by … and, for $0<k<n$, … For each positive integer $n$, let $\mathsf{APS}^B_n$ denote the set of admissible pinnacle sets for signed permutatio…

Shin–Zeng's conjecture. For $1\le k\le n$,

Let $B_n$ be the hyperoctahedral group of signed permutations, and for $\sigma\in B_n$ let $\mathsf{fwex}(\sigma)$, $\mathsf{\neg}(\sigma)$, $\mathsf{nest}_B(\sigma)$, and…

Cycle conjecture. The elements $n$ and $s_n$ are in the same cycle of $\pi$.

Cycle-membership conjecture. The elements $n$ and $s_n$ belong to the same cycle of $\pi$.

Cycle-membership conjecture. The elements $n$ and $s_n$ belong to the same cycle of $\pi$.

Let $s=(1,4,3,8,5,12,\ldots)$, with $s_{2i}=4i$ and $s_{2i-1}=2i-1$ for $i\geq 1$. Let $I_n$ be the set of $s$-inversion sequences of length $n$, and let $P_n$ be the set of signed…