## Free (tri)dendriform family algebras

International audience

International audience

In this paper, for each finite group $G$, we construct explicitly a non-compact complete finite-volume arithmetic hyperbolic $4$-manifold $M$ such that $\mathrm{Isom}\,M \cong G$, or $\mathrm{Isom}^{+}\,M \cong G$. In order to do so, we use essentially the geometry of Coxeter polytopes in the hyperbolic $4$-space, on one hand, and the combinatorics...

A word is u-quasiperiodic if a finite length word covers each of its index. The word u is called left (right) seed of a word w if u covers sw(ws) for a word s. The word u is called seed of a word w if u covers swt for the words s and t. We have found border, cover, left/right seed and seeds of Tribonacci words.

We characterize the topological configurations of points and lines that may arise when placing n points on a circle and drawing the n perpendicular bisectors of the sides of the corresponding convex cyclic n-gon. We also provide a functional central limit theorem describing the shape of a large realizable configuration of points and lines taken uni...

Nous introduisons les coordonnées cubiques, mots d'entiers codant les intervalles de Tamari. Les coordonnées cubiques sont en bijection avec les intervalle-posets, objets connus pour être eux-mêmes en bijection avec les intervalles de Tamari. Nous montrons que les ensembles de coordonnées cubiques forment des treillis isomorphes aux treillis des in...

We establish the following two main results on order types of points in general position in the plane (realizable simple planar order types, realizable uniform acyclic oriented matroids of rank 3):- The number of extreme points in an n-point order type, chosen uniformly at random from all such order types, is on average 4+o(1). For labeled order ty...

In the paper, by deriving an inequality involving the generating function of the Bernoulli numbers, the author introduces a new ratio of finite many gamma functions, finds complete monotonicity of the second logarithmic derivative of the ratio, and simply reviews complete monotonicity of several linear combinations of finite many digamma or trigamm...

Motivated by q-shuffle products determined by Singer from q-analogues of multiple zeta values, we build in this article a generalisation of the shuffle and stuffle products in terms of weak shuffle and stuffle products. Then, we characterise weak shuffle products and give as examples the case of an alphabet of cardinality two or three. We focus on ...

Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees. If the literature proposes solutions to enumerate singletons of trees, we study in this article a more general...

Given a graph $G=(V,E)$, $S\subseteq V$ is a dominating set if every $v\in V\setminus S$ is adjacent to an element of $S$. The Minimum Dominating Set problem asks for a dominating set with minimum cardinality. It is well known that its decision version is $NP$-complete even when $G$ is a claw-free graph. We give a complexity dichotomy for the Minim...