We consider two questions ofWilf related to Standard Young Tableaux. We provide a partial answer to one question, and that will lead us to a more general answer to the other question. Our answers are purely combinatorial.

We give a bijection between the symmetric group Sn, and the set of standard Young tableaux of rectangular shape mn, m > n, that have order n under jeu de taquin promotion.

We give a combinatorial description of the invariant factors associated with certain sequences of product of matrices, over a local principal ideal domain, under the action of the symmetric group by place permutation. Lascoux and Schützenberger have defined a permutation on a Young tableau to associate to each Knuth class a right and left key which they have used to give a combinatorial descrip...

Let SY Tn be the set of all standard Young tableaux with n cells. After recalling the definitions of four partial orders, the weak, KL, geometric and chain orders on SY Tn and some of their crucial properties, we prove three main results: • Intervals in any of these four orders essentially describe the product in a Hopf algebra of tableaux defined by Poirier and Reutenauer. • The map sending a ...

We show that Jn, the Stanley-Reisner ideal of the n-cycle, has a free resolution supported on the (n−3)-dimensional simplicial associahedron An. This resolution is not minimal for n > 6; in this case the Betti numbers of Jn are strictly smaller than the f -vector of An. We show that in fact the Betti numbers βd of Jn are in bijection with the number of standard Young tableaux of shape (d + 1, 2...

Unexpected product formulas for the number of standard Young tableaux of certain truncated shapes are found and proved. These include shifted staircase shapes minus a square in the NE corner, rectangular shapes minus a square in the NE corner, and some variations.

We define an inversion statistic on standard Young tableaux. We prove that this statistic has the same distribution over SY T (λ) as the major index statistic by exhibiting a bijection on SY T (λ) in the spirit of the Foata map on permutations.

This paper introduces calibrated representations for affine Hecke algebras and classifies and constructs all finite-dimensional irreducible calibrated representations. The primary technique is to provide indexing sets for controlling the weight space structure of finite-dimensional modules for the affine Hecke algebra. Using these indexing sets we show that (1) irreducible calibrated representa...

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.