7 problems

Let $A\subset\mathbb{Z}$ be a finite set of size $N$, and let $K>0$. Write $1_A$ for its indicator and define … A finite arithmetic progression is a finite subset of $\mathbb{Z}$ w…

Let $A$ be a set of $k\geq 4$ positive integers, and let $h$ be an integer with $3\leq h\leq k-1$. The restricted signed $h$-fold sumset is denoted by $h^{\wedge}_{\pm}A$. Bhanja–K…

Let $P_1,\dots,P_s\in\mathbb{Z}[x]$ be linearly independent polynomials that vanish at zero. Let $f_\omega:\mathbb{Z}/N\mathbb{Z}\to\mathbb{C}$ be one-bounded functions, and define…

Symmetrization conjecture. If

Griesmer's conjecture. Under these hypotheses, such compact subsets $A'$ and $B'$ exist. This conjecture proposes an inverse theorem for near equality in Kneser's inequality that e…

Let $A$ be a finite set of integers, and write $A-A=\{a-a':a,a'\in A\}$. Small-doubling structural conjecture. There exists a natural number $K$ such that, whenever $|A|\ge K$ and…

Károlyi's inverse Erdős–Heilbronn conjecture. The equality