We describe a probabilistic approach to a relatively new combinatorial object called staircase tableaux. Our approach allows us to analyze several parameters of a randomly chosen staircase tableau of a given size.

A new class of symmetric functions called factorial Schur symmetric functions has recently been discovered in connection with a branch of mathematical physics. We align this theory more closely with the s tandard symmetric function theory, giving the factorial Schur function a tableau definition, introducing a shift operator and a new generat ing function with which we extend to factorial symme...

We show that for all but two partitions λ of n > 6 there exists a standard tableau of shape λ with major index coprime to n. In conjunction with a deep result of Kraśkiewicz and Weyman this provides a new purely combinatorial proof of Klyachko’s famous theorem on Lie representations of the general linear group.

We prove a q-analog, which is valid if q is a positive real number, of the following: the probability that, when n tends to infinity, a randomly chosen standard Young tableau of size n contains a fixed standard Young tableau of shape λ ⊢ k is equal to f λ k! (Journal of Combinatorial Theory Series A, volume 97, 117–128, 2002). We also consider pairs of tableaux.

Lambda-Upsilon-Omega, , is a system designed to perform automatic analysis of well-deened classes of algorithms operating over \decomposable" data structures. It consists of an`Algebraic Analyzer' System that compiles algorithms speciica-tions into generating functions of average costs, and an`Analytic Analyzer' System that extracts asymptotic informations on coeecients of generating functions....

Youth is reserve force of sports development, is main force of Chinese sports further booming development sometime in the future. For Chinese three big balls, youth participation affects its development progress to a certain degree. Research youth preference way in three big balls movements’ participation is beneficial to sports teaching according to youth demands and then propel to Chinese thr...

Résumé. Ces dernières années, la classification croisée ou classification par blocs, c’est-à-dire la recherche simultanée d’une partition des lignes et d’une partition des colonnes d’un tableau de données, est devenue un outil très utilisé en fouille de données. Dans ce domaine, l’information se présente souvent sous forme de tableaux de contingence ou tableaux de co-occurrence croisant les mod...

The analytic signal of a real signal is a standard concept in 1D signal processing. However, the deenition of an analytic signal for real 2D signals is not possible by a straightforward extension of the 1D deenition. There rather occur several diierent approaches in the literature. We review the main approaches and propose a new deenition which is based on the recently introduced quaternionic F...