8 problems

Odd-coefficient convolution conjecture. For any integer $n\geq0$,

For positive integers $r$, $m$, and $p$, let $\{1\}_r$ denote the index consisting of $r$ successive entries equal to $1$, let $\zeta^\star$ denote a multiple zeta-star value, and…

For integers $a_0,\ldots,a_{2n}\geq 0$, let $eta^\star(s_1,\ldots,s_r)$ denote the multiple zeta star value, let $\operatorname{wt}$ denote the total weight of the arguments, and l…

For integers $n\geq 1$ and $j_1\geq 1$, $j_2,\ldots,j_n\geq 0$, let $\zeta^\star(k_1,\ldots,k_r)$ denote the multiple zeta-star value and let $\zeta^{1/2}(k_1,\ldots,k_r)$ denote t…

Weight-one insertion convolution conjecture. For any integer $n\geq1$,

Product identity conjecture. For any integers $n,m\geq0$,

Terminal-block symmetric sum conjecture. Let $n,j_0,\ldots,j_{2n}$ be non-negative integers and put $m=j_0+\cdots+j_{2n}$. Then

Symmetric sum conjecture. Let $n$ be a positive integer, let $j_0,\ldots,j_{2n-1}$ be non-negative integers, and put $m=j_0+\cdots+j_{2n-1}$. Then