Tilted Sperner Families
Imre Leader, Eoin Long
TL;DR
This paper investigates the maximum size of a family of subsets of an n-set that avoids pairs with a specific symmetric difference ratio, answering a question posed by Kalai and exploring related conjectures.
Contribution
It determines the maximum size of such families and presents related results and conjectures, advancing understanding of combinatorial set family constraints.
Findings
Identified the maximum size of families avoiding the specified subset pairs
Provided new bounds and exact results for certain cases
Proposed conjectures for further research
Abstract
Let \cal A be a family of subsets of an n-set such that \cal A does not contain distinct sets A and B with |A\B| = 2|B\A|. How large can \cal A be? Our aim in this note is to determine the maximum size of such an \cal A. This answers a question of Kalai. We also give some related results and conjectures.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Mathematical Dynamics and Fractals