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Preprint · arXiv · September 27, 2026

Binomial coefficients and the operadic butterfly

Vladimir Dotsenko, Medet Jumadildayev

Medet Jumadildayev
Read on arXivPDFDOI 10.48550/arxiv.2609.33480

Abstract

We prove the conjecture of Laubie on dimensions of components of two operads completing Loday's operadic butterfly diagram. For one of these operads, the dimension of the $n$-th component is equal to $\binom{2n}{n-1}$ for all $n\ne 3$, and for the other it is equal to $\binom{2n}{n-1}+1$ for all $n\ge 5$.

Homotopy and Cohomology in Algebraic TopologyAdvanced Combinatorial MathematicsAdvanced Topics in Algebraoperadsbinomial coefficientscombinatorial conjectures

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