A Bollob\'ass-type theorem on singular linear spaces
Erfei Yue, Benjian Lv, P\'eter Sziklai, and Kaishun Wang
TL;DR
This paper extends Bollobás-type theorems to singular linear spaces, establishing maximum sizes of Bollobás systems within this mathematical framework.
Contribution
It generalizes existing theorems from vector and affine spaces to singular linear spaces, providing new bounds on Bollobás systems.
Findings
Determined maximum cardinality of Bollobás systems in singular linear spaces.
Extended Bollobás-type theorems to a new class of mathematical structures.
Established bounds that unify previous results across different spaces.
Abstract
Bollob\'as-type theorem determines the maximum cardinality of a Bollob\'as system of sets. The original result has been extended to various mathematical structures beyond sets, including vector spaces and affine spaces. This paper generalizes the Bollob\'as-type theorem to singular linear spaces, and determine the maximum cardinality of (skew) Bollob\'as systems on them.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Banach Space Theory · Advanced Topics in Algebra