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Binomial coefficients and the operadic butterfly
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 binom2nn−1 for all n≠ 3, and for the other it is equal to binom2nn−1+1 for all n≥ 5.
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BibTeX
@misc{dotsenko2026binomial,
title = {{Binomial coefficients and the operadic butterfly}},
author = {Vladimir Dotsenko and Medet Jumadildayev},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33480},
eprint = {2609.33480},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33480},
}
RIS
TY - UNPB
TI - Binomial coefficients and the operadic butterfly
AU - Vladimir Dotsenko
AU - Medet Jumadildayev
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33480
UR - https://arxiv.org/abs/2609.33480
AB - 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 binom2nn−1 for all n≠ 3, and for the other it is equal to binom2nn−1+1 for all n≥ 5.
ER -