Compatible associative products and trees
Vladimir Dotsenko
TL;DR
This paper explores the structure of free algebras with two compatible associative products, providing dimension calculations and a combinatorial interpretation using planar rooted trees.
Contribution
It introduces a new combinatorial framework for understanding these algebras through planar rooted trees and computes their graded component dimensions.
Findings
Dimensions of graded components are explicitly computed.
A combinatorial interpretation via planar rooted trees is established.
Provides foundational results for compatible associative algebra structures.
Abstract
We compute dimensions of graded components for free algebras with two compatible associative products, and give a combinatorial interpretation of these algebras in terms of planar rooted trees.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology