13 problems

Let $\mathfrak B_n$ be the group of signed permutations, let $SR^B_n$ be the type $B$ superspace coinvariant ring, and let $\mathcal{OP}^B_n$ be the family of signed ordered set pa…

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…

Let $W_n$ be the group of signed permutations, and let $V_n$ be defined by … where … is the $k$th Catalan number. A signed permutation is vexillary if it avoids the nine signed pat…

Let $[n]^{\pm}$ be the signed set, and let … and … be long cycles on $[n]^{\pm}$. Set $\pi=p\circ s$. Chen–Reidys cycle conjecture. The elements $n$ and $s_n$ belong to the same cy…

Unimodality and monotonicity conjecture. Every row in $D$ and in $\widetilde{D}$ is a unimodal sequence. For every $k\geq 1$, the sequences

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…