The operad Lie is free
Paolo Salvatore, Roberto Tauraso
TL;DR
This paper proves that the operad Lie is free as a non-symmetric operad and analyzes the generating series for its generators, revealing a recursive formula and an asymptotic density of 1/e.
Contribution
It establishes the freeness of the operad Lie in the non-symmetric setting and provides a detailed combinatorial analysis of its generators.
Findings
Operad Lie is free as a non-symmetric operad.
Derived a recursive formula for the generating series coefficients.
Showed the asymptotic density of generators approaches 1/e.
Abstract
We show that the operad Lie is free as a non-symmetric operad. Then we study the generating series counting the operadic generators, finding a recursive formula for its coefficients, and showing that the asymptotic density of the operadic generators is 1/e.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics