123 problems

Let $s\geq 3$ be an integer. An $s$-spanning set of size $2$ in a finite abelian group is a set of two elements whose signed sums of at most $s$ terms cover the group. Largest nonc…

Let $G$ be a finite abelian group, let $\mathcal A(G)$ denote the set of minimal zero-sum sequences over $G$, and let ${\rm D}(G)$ denote the Davenport constant. A set…

Characterization conjecture. If $\mathsf D(G)\geq 4$, then $G$ and $G'$ are isomorphic.

Let $p$ be a prime, and let $s_1(Z_p^3)$ denote the least integer $\ell$ such that every sequence of length $\ell$ in the finite abelian group $Z_p^3$ contains a zero-sum subsequen…

Let $G$ be a finite Abelian group, let $V_g f$ denote the time-frequency representation appearing in the paper, let $\widehat f$ denote the Fourier transform of $f$, and write…

Let $n>1$ be a positive integer, and let $p$ be the smallest prime divisor of $n$. For positive integers $n$ and $k$, let … where $S$ ranges over sequences in $\mathbb{Z}_n$ of len…

For an integer $n\geqslant2$, let $\mathbb{Z}_{\!/2}^n$ denote the direct sum of $n$ copies of the cyclic group $\mathbb{Z}_{\!/2}$. Let $\lambda(\mathbb{Z}_{\!/2}^n)$ denote its L…

For an integer $n\geqslant2$, let $\rho(n)$ denote the smallest prime number that does not divide $n$. For the cyclic group $\mathbb{Z}_{\!/n}$, let $\lambda(\mathbb{Z}_{\!/n})$ de…

Let $n_1\geq n_2$ be positive integers, let $0<u<1$, and let $G(n_1,n_2,u)$ be the Erdős–Rényi random bipartite graph whose bipartition has vertex sets of sizes $n_1$ and $n_2$, wi…

Higher-rank square-modulus conjecture. For every odd prime $p$ and every $r\geq 1$,

Odd square-plane conjecture. For every odd prime $p$,

Relative Davenport equality conjecture. One has

Let $k$ be a positive integer and write $S(k)=\{1,2,\dots,k\}$. Let $G$ be a finite abelian group. Say that $S(k)$ splits $G$ if there is a subset $T\subseteq G$ such that the tran…

Schefler56Zhao56Zhong's conjecture. The support of $A$ has full size:

Gallardo–Grekos–Pihko conjecture. There is a constant $c$ such that, whenever

Gao's conjecture. For every finite abelian group $G$, one has

Let $\mathcal{A}_3$ and $\mathcal{B}_3$ be the classes of finite abelian groups arising in the paper, and let … while … where $G_1=(\mathbb{Z}/4)^4$,…

Let $G$ be a finite abelian group with $|G|>4$. Write $\rho(G)$ for its elasticity and let $\Delta{\rho}(G)$ be the set of all $dinmathbb N$ such that, for every $kinmathbb N$, ther…

Balister–Győri–Schelp conjecture. There exists a partition of $\mathbb F_2^k$ into 2-sets $\{w_i,z_i\}$, for $i\in\{1,\dots,2^{k-1}\}$, such that

Let $G$ be a finite abelian group with rank $r(G)\geq 2$ and $\mathsf{D}(G)=\mathsf{D}^*(G)$. Let $k$ be a positive integer with $\mathsf{D}(G)-k\in[\exp(G),\mathsf{D}(G)]$. Let…

Let $G$ be a finite abelian group with rank $r(G)\geq 2$ and $\mathsf{D}(G)=\mathsf{D}^*(G)$, and let $\exp(G)$ denote its exponent. Let $\mathsf{s}_{\leq m}(G)$ be the smallest le…

Non-elementary group conjecture. For any $(k,x)$ with $1\le k\le n-1$ and $x\in G$, the incidence structure $(G,\mathcal{B}_k^x)$ is not a $2$-design.

Mészáros's critical-distribution conjecture. For every finite abelian $p$-group $G$,

Let $({\mathcal A},{\mathcal B})$ be a distributed spectral pair in $\{0,1,\ldots,M-1\}$. A distributed spectral pair classification conjecture. The pair…

Let $\overrightarrow{G}$ be a digraph of order $n$ whose weakly connected components all have order at least $3$, and let $\Gamma$ be an Abelian group. A $\Gamma$-irregular labelin…