13 problems

Fix $z,d,w\in\mathbb{Z}_{>0}$ with $z<d$, and assume that … for all $z'\leq z$, $d'<d$, and $w'<w$. For every $\mathbf{k}=(k_1,\ldots,k_d)\in\mathbb{Z}_{>0}^d$ and every word…

Basis conjecture. For $1\leq z\leq d$, $\mathfrak{B}_{z,d}$ is a basis of $\mathscr{S}_{z,d}$. The set was obtained from numerical calculations, and the paper postpones a proof to…

For positive integers $z,d$ with $z\leq d$, let $\mathcal{K}_{z,d}$ and $\operatorname{Box}_{z,d}$ be as defined in the source. Basis conjecture. If $z\leq d$, then…

For positive integers $z,d$, let $\mathcal{K}_{z,d}$ be the explicitly defined subspace of the domain of the box map $\operatorname{Box}_{z,d}$ generated by the stuffle–box-product…

For positive integers $z,d$, let $\mathscr{S}_{z,d}$ be the $\mathbb{Q}$-span of the box products $u_{\mathbf n}\boxast u_{\boldsymbol\ell}$ with…

Refined Bachmann conjecture. For all $z,d,w\in\mathbb{Z}_{>0}$,

Bachmann's conjecture. All $\mathbb{Q}$-linear relations among elements of $\mathcal{Z}_q$ are generated by the stuffle product $\ast$ and duality $\tau$. This conjecturally gives…

Refinement of Bachmann's conjecture. There exist polynomials $Q_j\in\mathbb{Q}[X_1,\dots,X_j]$, for $j\geq 1$, with $Q_j\equiv 0$ for all but finitely many $j$, such that for every…

Okounkov's conjecture. We have

Bachmann's conjecture. We have

Let a collection consist of mono- or bi-brackets, viewed as elements of the relevant bracket algebra over $\mathbb Q$ and $\mathbb C(q)$. Rationality conjecture for bracket relatio…

Let bi-brackets be the $q$-multiple zeta values defined in the paper, equipped with their stuffle and dual stuffle products and the duality relation. Bachmann's double stuffle conj…

Let $\operatorname{\mathsf{qMZV}}$ denote the algebra of $q$-multiple zeta values, containing the ring of quasi-modular forms $\widetilde{M}_{\mathbb{Q}}=\mathbb{Q}[G_2,G_4,G_6]$,…