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arXiv · 2609.33480

Binomial coefficients and the operadic butterfly

Vladimir Dotsenko·Medet Jumadildayev
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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 $n\ge 5$.

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Vladimir Dotsenko, Medet Jumadildayev. 2026-09-27. Binomial coefficients and the operadic butterfly. https://arxiv.org/abs/2609.33480

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