A. Fish

activity

20052026

most citedCharacteristic Polynomial Patterns in Difference Sets of Matrices

7 citations · 28 across the 31 of their papers we have counts for

collaborators

37 papers

math.MG2026

On determination of convex bodies by their section functions

Alexander Fish, Dmitry Ryabogin, Wen Rui Sun +1

For a convex body $K$ its parallel section function in the direction $θ \in S^{n - 1}$ is defined by $$A_{K,θ}(t) = \mathrm{vol}_{n-1} \left( K \cap \{ x \in \mathbb{R}^n ~ | ~ \langl…

math.DS2022

Glasner property for linear group actions and their products

Kamil Bulinski, Alexander Fish

A theorem of Glasner from 1979 shows that if $Y \subset T = R / Z$ is infinite then for each $ε > 0$ there exists an integer $n$ such that $nY$ is $ε$ -dense…

math.CO2021

Arithmetic subtrees in large subsets of products of trees

Kamil Bulinski, Alexander Fish

Furstenberg-Weiss have extended Szemerédi's theorem on arithmetic progressions to trees by showing that a large subset of the tree contains arbitrarily long arithmetic subtrees. We…

math.DS2021

Reconstructing a minimal topological dynamical system from a set of return times

Kamil Bulinski, Alexander Fish

We investigate to what extent a minimal topological dynamical system is uniquely determined by a set of return times to some open set. We show that in many situations this is indee…

math.DS2021

Glasner property for unipotently generated group actions on tori

Kamil Bulinski, Alexander Fish

A theorem of Glasner from 1979 shows that if $A \subset T = R / Z$ is infinite then for each $ε > 0$ there exists an integer $n$ such that $n A$ is $ε$ -dense…

math.NT2021

On almost Cap sets in three variables and the multivariable Cap set problem

Alexander Fish, Dibyendu Roy

In this note we prove that almost cap sets $A \subset F_{q}^{n}$ , i.e., the subsets of $F_{q}^{n}$ that do not contain too many arithmetic progressions of length three, s…