13 problems

Gaussian-product unimodality conjecture. For every $0\leq k<n$, this polynomial is symmetric and unimodal. The source states that, using known results together with its preceding t…

Let $B_N$ be the hyperoctahedral group and let $V=V_{((N-1),(1))}$ be its natural representation. Let $T(B_N,V)$ be the tensor product graph, let $I(V)$ denote its identity represe…

Cesi's conjecture.

Let $v,w\in\mathfrak{B}_n$ avoid the patterns $3412$ and $4231$. Write $\Gamma(v)$ and $\Gamma(w)$ for their type-$\mathsf{BC}$ indifference graphs, and let…

Let $B_n$ be the hyperoctahedral group, let $(theta, u)$ be a bipartition in $operatorname{BP}n$, and let $I{(theta,nu)}$ denote the corresponding $Bn$-Specht ideal. For bipartitio…

Let $\overline{\operatorname{OST}}_{n,\alpha}$ be the biased one-sided transposition shuffle on the hyperoctahedral group with weight $w(j)=j^\alpha$, and let $t_{n,\alpha}$ be the…

Let $B_n$ be the hyperoctahedral group, and let $\overline{\operatorname{RT}}_n$ denote its random transposition shuffle. Upper-bound conjecture. The shuffle has a total variation…

Signed odd-length factorization conjecture.

Varchenko–Stasinski's conjecture. The generating function satisfies

Let $n\in\mathbb P$, let $i\in[3,n-1]$, and define … Here $D_n^{\{0,1,i\}}$ is the corresponding quotient of the even hyperoctahedral group, $\ell$ is Coxeter length, and $L$ is th…

Odd-length factorization conjecture. For the quotients considered in the paper, these signed generating functions should factor in a very nice way.

Stasinski and Voll's conjecture. The polynomial $xt+1$ divides

Stasinski–Voll's conjecture. For every $n\in\mathbb{N}$ and every $I=\{i_1,\dots,i_l\}_{<}\subseteq[n-1]_0$,