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We introduce $k$-signaletic operads and their Koszul duals, generalizing the dendriform, diassociative and duplicial operads (which correspond to the $k=1$ case). We show that the Koszul duals of the $k$-signaletic operads act on multipermutations and that the resulting algebras are free, thus providing combinatorial models for these operads. Finally, motivated by these actions on multipermutations, we introduce similar operations on multiposets which yield yet another relevant operad obtained as Manin powers of the $L$-operad., Comment: 97 pages, 20 figures

Phylogenetic trees are binary non-plane trees with labelled leaves, and plane oriented recursive trees are planar trees with an in- creasing labelling. Both families are enumerated by double factorials. A bijection is constructed, using the respective representations as 2- partitions and trapezoidal words.

Given the toric (or toral) arrangement defined by a root system $\Phi$, we describe the poset of its layers (connected components of intersections) and we count its elements. Indeed we show how to reduce to zero-dimensional layers, and in this case we provide an explicit formula involving the maximal subdiagrams of the affine Dynkin diagram of $\Phi$. Then we compute the Euler characteristic and the Poincare' polynomial of the complement of the arrangement, which is the set of regular points of the torus., Comment: 20 pages. Updated version of a paper published in December 2008