8 problems

Minimal-period conjecture. The minimum period of $c_j(k)$ is $p_j$ for every $0\leq j\leq d$. This conjecture predicts that the divisibility data of the $a_i$ determine the exact p…

Let $r,D\geq 1$ be integers, and let $\Delta_{r,D}$ denote the determinant of the linear system obtained from the Bernoulli-polynomial identities for the coefficients of the restri…

Let $S(2\mathbb{N}-1,n)$ denote the difference between the sums of the odd and even parts over partitions of $n$ into distinct parts from $2\mathbb{N}-1$. The mod 7 congruence conj…

Let $m_1,m_2\in\mathbb N$, let $p\geq 3$, and let $V(m_1)$ and $V(m_2)$ denote the corresponding $SL_2$-modules. The extension space is $\operatorname{Ext}^n_{SL_2}(V(m_2),V(m_1))$…

Let $r(x)$ be the generating function whose coefficients $f_{O_j}(k)$ count the relevant partitions into fractions with fixed denominator $j$, with $k$ ranging over the integer val…

Let $j>2$ and let $k,j\in\mathbb{N}$. For a sequence of numerators $\{n_j\}$, define … A sequence enables solutions when every positive integer $k<\lfloor G\rfloor$ can be represen…

Let $D\geq 2$, and let $\bar F_{2,D}(x_1,\ldots,x_D)$ be the determinant polynomial defined in the paper for $r=2$. Quadratic-index factorization conjecture. There is a rational co…

Let $r,D\geq 1$, and let $\Delta_{r,D}$ denote the determinant defined in the paper from Bernoulli polynomials. Nonvanishing conjecture. The determinant is nonzero: … This conjectu…