TL;DR
This paper explores the structure of paths in the Farey graph and Stern-Brocot tree, revealing operad formations and identifying special 'corona' paths with unique properties.
Contribution
It introduces the concept of operads in the context of Farey graph paths and characterizes 'coronas' as significant spiked paths within these structures.
Findings
Paths form an operad structure.
Coronas are identified as spiked paths.
Certain sets are proven to be coronas.
Abstract
We study the paths in the Farey graph going from (1,0) to (0,1) , or the finite subtrees of the Stern-Brocot tree . We show they form an operad and isolate the "coronas", which are especially spiked paths. We show that {(x,y), gcd(x,y)=1 , x+y < R } is a corona.
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