2 problems

Let $\mathcal{P} ois$ denote the Poisson operad, $\mathcal{Z} inb$ the Zinbiel operad, and $pre\mathcal{P} ois$ and $pre\mathcal{L} ie$ the corresponding pre-operads. Let $\circ$ d…

An $L$-dendriform algebra is a vector space equipped with two operations $x\prec y$ and $x\succ y$ satisfying … … where $x * y=x\prec y+x\succ y$. Vallette's conjecture. The operad…