7 problems

Gaussian-product unimodality conjecture
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…
openFrom papershyperoctahedral-groups q-enumeration unimodality
0 responses
15
The $\gamma_2$ -character bridge conjecture for the hyperoctahedral group
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…
openFrom papershyperoctahedral-groups quantum-query-complexity representation-theory
0 responses
10
Cesi's spectral-gap conjecture for the hyperoctahedral group
Cesi's conjecture.
openFrom papershyperoctahedral-groups representation-theory spectral-gaps
0 responses
40
The type-BC indifference graph equivalence conjecture for Kazhdan–Lusztig basis elements
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…
openFrom papershyperoctahedral-groups kazhdan-lusztig-theory trace-functions
0 responses
10
Varchenko–Stasinski's conjecture on odd-length generating functions for type B parabolic quotients
Varchenko–Stasinski's conjecture. The generating function satisfies
openFrom papersgenerating-functions hyperoctahedral-groups weyl-groups
0 responses
5
Stasinski and Voll's hyperoctahedral group factorization conjecture
Stasinski and Voll's conjecture. The polynomial $xt+1$ divides
openFrom papershyperoctahedral-groups length-generating-functions parabolic-quotients
0 responses
3
Stasinski–Voll's signed $L$ -generating-function conjecture for hyperoctahedral descent classes
Stasinski–Voll's conjecture. For every $n\in\mathbb{N}$ and every $I=\{i_1,\dots,i_l\}_{<}\subseteq[n-1]_0$ ,
openFrom papersgenerating-functions hyperoctahedral-groups permutation-statistics
0 responses
4

7 problems

Gaussian-product unimodality conjecture

The γ2\gamma_2γ2​-character bridge conjecture for the hyperoctahedral group

Cesi's spectral-gap conjecture for the hyperoctahedral group

The type-BC indifference graph equivalence conjecture for Kazhdan–Lusztig basis elements

Varchenko–Stasinski's conjecture on odd-length generating functions for type B parabolic quotients

Stasinski and Voll's hyperoctahedral group factorization conjecture

Stasinski–Voll's signed LLL-generating-function conjecture for hyperoctahedral descent classes

The $\gamma_2$ -character bridge conjecture for the hyperoctahedral group

Stasinski–Voll's signed $L$ -generating-function conjecture for hyperoctahedral descent classes