21 problems

Let $M(\bs;\varepsilon)$ denote a multiple mixed value and $T(\bs)$ a multiple t-value. Classify indices as wide, slender, or narrow according to whether their largest component is…

Let $M(\bs;\varepsilon)$ denote a multiple mixed value and $T(\bs)$ a multiple t-value. Classify indices as wide, slender, or narrow according to whether their largest component is…

Let $M(\bs;\varepsilon)$ denote a multiple mixed value of depth $4$, let $T(\bs)$ denote a multiple t-value, and classify indices as wide, slender, or narrow by whether their large…

Let $\bfs$ be an index, let $T(\bfs)$ be a multiple t-value (MTV), and let $\bfs^*$ be its dual. Define the width $\operatorname{wth}(\bfs)$ as the largest component of $\bfs$; cal…

Let $a,b\in\mathbb{Z}_{\geq 0}$, and define … where $t(s_1,\ldots,s_r)$ is the multiple $t$-value over positive odd integers. Lupu's conjecture for $T(a,b)$. For nonnegative intege…

Let $a,b\in\mathbb{Z}_{\geq 0}$, and let $H(a,b)$ denote the quantity used in Lupu's Zagier-type formula for multiple $t$-values. Lupu's conjecture for $H(a,b)$. For nonnegative in…

Let $\mathsf{FMT}_w$ be the $\mathbb{Q}$-vector space generated by finite multiple $T$-values of weight $w$. Finite multiple $T$-value dimension conjecture. For all $k\geq1$, … Thi…

Let $S_{\mathcal A}$ and $S_\shuffle^{\mathcal S}$ denote the finite and shuffle-regularized symmetric $S$-values, respectively. Even all-ones S-value conjecture. For every even…

Let $T_{\mathcal A}$ and $T_\shuffle^{\mathcal S}$ denote the finite and shuffle-regularized symmetric multiple $T$-values, respectively; let $S_{\mathcal A}$ and…

Kaneko–Tsumura's conjecture. For even weights, the values $T(k,l,m)$ with $k,r$ odd and at least $3$ and $q$ even, together with their duals, are in $MZV$. Together with the single…

Let $t^{\sfrac{1\!}{2}}(2,\{1\}^{2n+1},2)$ denote the multiple $t$-value with the indicated indices, and let $t(k)$ denote the ordinary $t$-value of weight $k$. Odd-weight evaluati…

Conjecture on singular regularisation parameters. The sequence is increasing and bounded by $3$:

Let $N\in\mathbb{N}$, and write $t(\{2\}^N,1)$ for the multiple $t$-value with $N$ consecutive entries equal to $2$, followed by $1$. Let $I(2N)$ and $\eta(s)$ denote the quantitie…

Let $(d_n)_{n\geqslant1}$ be the Padovan sequence defined by $d_1=0$, $d_2=1$, $d_3=1$ and $d_n=d_{n-2}+d_{n-3}$ for $n\geqslant4$, and let $(f_n)_{n\geqslant1}$ be the Fibonacci s…

Let $\mathcal{Z}_k$ be the weight-$k$ space of ordinary multiple zeta values. For a sequence $(k_1,\ldots,k_r)$, call it Lyndon when every proper right subsequence is greater than…

Let $T(p+i,q+j)$ denote a double multiple $T$-value, with $m\geq 1$, $p\geq 1$, and $q\geq 2$. Assume that $p+q+m$ is even. The parity-weighted double $T$-value conjecture. … The c…

Let $T(p,q,r)$ denote a triple multiple $T$-value, let $T(k)$ denote a single $T$-value, and let $\mathcal{Z}$ be the space of ordinary multiple zeta values. By duality, restrict t…

Let $\mathcal{Z}$ be the space of ordinary multiple zeta values, and let $\mathcal{T}^{\sh}$ and $\mathcal{T}^*$ be the shuffle and stuffle spaces of multiple $T$-values. The conta…

Let $T(a,b,c)$ denote the multiple $T$-value of indices $(a,b,c)$, and let $T(k)$ denote the single $T$-value of weight $k$. For $k\geq 4$, the indices satisfy $a+b+c=k$, with…

Let $\mathcal T$ be the $\mathbb Q$-subalgebra of $\mathbb R$ generated by $1$ and the multiple $t$-values, and let $\mathcal T_n$ be the subspace of $\mathcal T$ spanned by all mu…

Let $\operatorname{QSym}$ be the algebra of quasisymmetric functions, let $A_-:\operatorname{QSym}\to\operatorname{QSym}$ be the derivation defined by $A_-(1)=0$ and … let…