arXiv subjects

Máté Pálfy

Publications and source records attributed to Máté Pálfy.

5 recordsLinked to original sources

arXiv2025

Generic properties of topological groups

We study generic properties of topological groups in the sense of Baire category. First we investigate countably infinite (discrete) groups. We extend a classical result of B. H. Neumann, H. Simmons and A. Macintyre on algebraically closed groups and the word problem. I. Goldbring, S. E. Kunnawalkam and Y. Lodha proved that every isomorphism class is meager among countably infinite (discrete) groups. In contrast, we show that there is a comeager isomorphism class among countably infinite (discrete) abelian groups. Then we turn to compact metrizable abelian groups. We use Pontryagin duality to show that there is a comeager isomorphism class among compact metrizable abelian groups. We discuss its connections to the countably infinite (discrete) case. Finally, we study compact metrizable groups. We prove that the generic compact metrizable group is neither connected nor totally disconnected; also it is neither torsion-free nor a torsion group.

math.LO↗

arXiv2025

Generic isomorphism classes of abelian groups

We prove that the universal solenoid is the generic (in the sense of Baire category) connected compact metrizable abelian group. We also settle the dual problem in the sense of Pontryagin duality: $(\mathbb{Q},+)$, which is the dual of the universal solenoid, is the generic countably infinite torsion-free abelian group.

math.LO↗

arXiv2024

On the structures of subset sums in higher dimension

A given subset $A$ of natural numbers is said to be complete if every element of $\N$ is the sum of distinct terms taken from $A$. This topic is strongly connected to the knapsack problem which is known to be NP complete. The main goal of the paper is to study the structure of subset sums in a higher dimension. We show 'dense' sets and generalized arithmetic progrssions in subset sums of certain sets.

math.CO↗

arXiv2022

Compact Lie groups isolated up to conjugacy

The set $\mathcal S(G)$ of compact subgroups of a Hausdorff topological group $G$ can be equipped with the Vietoris topology. A compact subgroup $K\in\mathcal S(G)$ is isolated up to conjugacy if there is a neighborhood $\mathcal U\subseteq\mathcal S(G)$ of $K$ such that every $L\in\mathcal U$ is conjugate to $K$. In this paper, we characterize compact subgroups of a Lie group that are isolated up to conjugacy. Our characterization depends only on the intrinsic structure of $K$, the ambient Lie group $G$ and the embedding of $K$ into $G$ are irrelevant. In addition, we prove that any continuous homomorphism from a compact group $G$ onto a compact Lie group $H$ induces a continuous open map from $\mathcal S(G)$ onto $\mathcal S(H)$.

math.DG↗

arXiv2021

On a Communication Complexity problem in Combinatorial Number Theory

The original knapsack problem is well known to be NP-complete. In a multidimensional version one have to decide whether a $p\in \N^k$ is in a sumset-sum of a set $X \subseteq \N^k$ or not. In this paper we are going to investigate a communication complexity problem related to this.

cs.DM↗