Closed formulas are known for S(k, 0; n), the number of standard Young tableaux of size n and with at most k parts, where 1 ≤ k ≤ 5. Here we study the analogous problem for S(k, ℓ; n), the number of standard Young tableaux of size n which are contained in the (k, ℓ)-hook. We deduce some formulas for the cases k + ℓ ≤ 4.

There are several results concerning double cosets of Young subgroups of symmetric groups which are often proved as corollaries of more general results about Coxeter groups. In this note we give a selection of these results and give them short combinatorial proofs. The replacement for the machinery of Coxeter groups consists of some simple combinatorial arguments involving tableaux. Inevitably ...

RÉSUMÉ. Dans cet article, nous présentons les résultats obtenus par un détecteur de tableau dans le cadre des campagnes MAURDOR, pour lesquelles le corpus présente la particularité de contenir des document fortement hétérogènes dans leur mise en page, leurs scripts et les langues utilisées. ABSTRACT. This paper presents the results obtained by a table detector during the MAURDOR campaign, the c...

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.

Ji et al. have conjectured that using the matrix form (to represent a basic solution) instead of the Simplex tableau in the dual Simplex method will lead to an algorithm with the time complexity comparable to the Hungarian algorithm for solving the Assignment Problem. In this note we show that both the time complexity and the CPU times of the Ji et al. algorithm are far away from being competit...

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...