Sur une conjecture de Dehornoy

Sur une generalisation des coefficients binomiaux

We prove a recent conjecture of Lassalle about positivity and integrality of coefficients in some polynomial expansions. We also give a combinatorial interpretation of those numbers. Finally, we show that this question is closely related to the fundamental problem of calculating the linearization coefficients for binomial coefficients.

关于Matula Arborification的一则注记

Une remarque sur l'arborification de Matula

本文提出利用Matula的arborification方法研究自然数上莫比乌斯和利乌维函数的部分和，揭示其数论性质。

A lattice of combinatorial Hopf algebras, Application to binary trees with multiplicities

In a first part, we formalize the construction of combinatorial Hopf algebras from plactic-like monoids using polynomial realizations. Thank to this construction we reveal a lattice structure on those combinatorial Hopf algebras. As an application, we construct a new combinatorial Hopf algebra on binary trees with multiplicities and use it to prove a hook length formula for those trees. Dans une première partie, nous formalisons la construction d'algèbres de Hopf combinatoires à partir d'une réalisation polynomiale et de monoïdes de type monoïde plaxique. Grâce à cette construction, nous metto…

Sur une proprieté des polynômes de Stirling

In this article, we give a positive answer to a question posed in 1960 by D.S. Mitrinović and R.S. Mitrinović (see: D.S. Mitrinović et R.S. Mitrinović, Tableaux qui fournissent des polynômes de Stirling, Publications de la Faculté d'Electronique, série: Mathématiques et physique, 34, (1960).1-23.) concerned the Stirling numbers of the first kind $s(n,k).$ We prove that for all $k\geq 2$ there exist an integer $m_{k}$ and a primitive polynomial $P_{k}(x)$ in $\mathbb{Z}[x]$ such that for all $n\geq k$, $s(n,n-k)=\frac{1}{m_{k}}\binom{n}{k+1}\left(n(n-1)\right) ^{\mathop{\rm mod}\nolimits (k,2)}…