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...

Let μ be a partition of k, and T a standard Young tableau of shape μ. McKay, Morse, and Wilf show that the probability a randomly chosen Young tableau of N cells contains T as a subtableau is asymptotic to fμ/k! as N goes to infinity, where fμ is the number of all tableaux of shape μ. We use a random-walk argument to show that the analogous asymptotic probability for randomly chosen Young table...

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.