15 problems

Costa–Morini–Pasotti–Pellegrini conjecture. For any abelian group $(G,+)$ and any subset $A\subseteq G\setminus\{0\}$ such that there is no $x\in A$ with $\{x,-x\}\subseteq A$ and…

Archdeacon–Dinitz–Mattern–Stinson conjecture. For any cyclic group $\mathbb{Z}_n$ and any subset $A\subseteq\mathbb{Z}_n\setminus\{0\}$, there is an ordering of the elements of $A$…

Let $k$ be fixed, and let $A$ be a $k$-element subset of the nonzero elements of ${\mathbb Z}_n$. Fixed-size sequencing problem. Determine whether there exists a constant $N$ such…

Helson's conjecture. The expected absolute value of the partial sum should exhibit better-than-square-root cancellation:

CMPP conjecture. There exists an ordering of the elements of $A$ such that all partial sums are distinct.

G-ADMS conjecture. There exists an ordering of the elements of $A$ such that all partial sums are distinct.

Alspach's conjecture. If

Let $\mathcal{R}(\alpha,\beta)$ be the class of normalized analytic functions $f$ in the unit disk $\Delta$, with parameters $-\pi<\alpha\leq\pi$ and $0\leq\beta<1$. For…

Koumandos–Ruscheweyh weaker conjecture. For every $z\in\mathbb{D}$, $n\in\mathbb{N}$, and $0<\mu\leq\mu^{\ast}(\rho)$,

Let $A$ be a $k$-element subset of the nonzero elements of ${\mathbb Z}_n$, and let the partial-sum sequencing conjecture be the assertion that $A$ has an ordering with pairwise di…

Let $p$ be a prime and let $S$ be a multiset containing $p-1$ nonzero elements of ${\mathbb Z}_p$. Buratti's conjecture. There exists an arrangement of the elements of $S$ such tha…

Let $A=a_1,ots,a_k$ be a subset of the nonzero elements of ${\mathbb Z}_n$. For an ordering $(a_1,\ldots,a_k)$ of $A$, define the partial sums by … with arithmetic in…

Let ${\mathcal{F}}$ be the class of locally univalent functions $f$ in ${\mathcal A}$ satisfying … For $f(z)=z+\sum_{k=2}^{\infty}a_kz^k$, let $s_n(f)(z)=z+\sum_{k=2}^{n}a_kz^k$ be…

Let ${\mathcal{F}}$ be the class of locally univalent functions $f$ in ${\mathcal A}$ satisfying … For $f(z)=z+\sum_{k=2}^{\infty}a_kz^k$, let $s_n(f)(z)=z+\sum_{k=2}^{n}a_kz^k$ be…

Erdős's conjecture. The partial sums of $f$ should be unbounded: