30 problems

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 $\mathcal T$ 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 $\mathsf{AMTV}_w$ be the $\mathbb{Q}$-vector space generated by all alternating multiple $T$-values of weight $w$, and write $d_w=\dim_{\mathbb{Q}}\mathsf{AMTV}_w$ for…

For a finite admissible multi-index, the multiple $t$-value is defined by … The weight of a multi-index is $k_1+\cdots+k_d$, and multiple $t$-values of weight $n$ span a vector spa…

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…

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 $\bfs$ be an index and let $\bfs^*$ denote its dual. Let $T(\bfs)$ be a multiple t-value (MTV), and call it unramified when it belongs to the unramified class considered in the…

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 $\mathsf{AMT}_w$ be the $\mathbb{Q}$-vector space generated by alternating multiple $T$-values of weight $w$. Xu–Zhao tribonacci conjecture. With strong numerical support, the…

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…

Let $T(2,1,\ldots,1,\overlineO{\mathclap{\phantom{I}}1})$ denote the multiple $T$ value with first argument $2$, subsequent arguments equal to $1$ except for a possible alternating…

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 $3$:

Saha's basis conjecture. The set $\mathcal{B}^S$ is a basis for the space of convergent multiple $t$-values. Its weight-$w$ component has cardinality $\#{\mathcal{B}_N^S}=F_N$ for…

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 $t(\mathbf{k})$ denote the multiple $t$-value associated with an admissible or empty multi-index, and let $\Phi$ be the previously defined bijection from the ordered set of mul…

Let $\mathcal{T}^{\sh}_5$ denote the shuffle space of multiple $T$-values of weight $5$. The weight-five dimension conjecture. … The source explains that, using duality and known r…