2-Segal sets from cuts of rooted trees

TL;DR

This paper constructs 2-Segal sets from rooted trees, illustrating their connections to algebraic K-theory, Hall algebras, and operads, and explores their applications in these areas.

Contribution

It introduces a novel method of deriving 2-Segal sets from rooted trees, expanding their applicability in algebraic and combinatorial contexts.

Findings

Constructed 2-Segal sets from rooted trees

Demonstrated applications to algebraic K-theory and Hall algebras

Provided insights into operad-related structures

Abstract

The theory of 2-Segal sets has connections to various important constructions such as the Waldhausen $S_\bullet$-construction in algebraic $K$-theory, Hall algebras, and (co)operads. In this paper, we construct 2-Segal sets from rooted trees and explore how these applications are illustrated by this example.