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This is a Quantitative Study study.

September 24, 2025Open Access

Separating subsets from their images

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The study derives general bounds for the parameter in transitive permutation groups, revealing limits on subset sizes.
Asymptotic behaviour of certain families of primitive groups is examined, highlighting significant patterns in set behavior.
Introducing the parameter $ ext{m}(G)$ reflects the structure and interaction within subsets of group points.
Understanding these bounds could lead to advancements in combinatorial group theory and applications in symmetry.

Implication

This paper studies a parameter estimating largest disjoint subsets in transitive groups, indicating bounds and behaviors.

Abstract

Let G be a transitive permutation group. In this paper, we introduce and study the parameter (G), which estimates the size of the largest set of points A such that there exists a permutation g with the property that A ∩ Aᵍ is empty. In particular, we focus on deriving general bounds for arbitrary transitive groups, and on the asymptotic behaviour of certain families of primitive groups.

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Cite This Study

Barbieri et al. (2025) studied this question.

synapsesocial.com/papers/68d6e0fc8b2b6861e4c3f5fd https://doi.org/10.48550/arxiv.2508.20731

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Implication

This paper studies a parameter estimating largest disjoint subsets in transitive groups, indicating bounds and behaviors.

Separating subsets from their images

Key Points

Implication

Abstract

Discussion

Cite This Study

Separating subsets from their images

Key Points

Implication

Abstract

Discussion

Cite This Study

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