Greedy capsets
Oliver Dawson, Oleg Shuvaev, Jos\'e Felipe Voloch
TL;DR
This paper characterizes the process of constructing capsets in finite vector spaces by iteratively removing points with the maximum number of lines, culminating in a line-free set.
Contribution
It introduces a novel greedy method for constructing capsets by successively removing points with the highest line count, providing new insights into their structure.
Findings
The process terminates with a line-free set.
The characterization links removal order to capset structure.
Provides a new perspective on capset formation.
Abstract
A capset is a subset with no three points on a line. We characterise the capsets produced by successively removing points from the ambient space such that the removed point has the maximum number of lines contained in the set of remaining points and passing through it until the set of remaining points contains no lines.
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Taxonomy
TopicsProtein Degradation and Inhibitors