A well-known theorem of Frame, Robinson, and, Thrall states that if h is a partition of n, then the number of Standard Young Tableaux of shape h is n! divided by the product of the hook-lengths. We give a new combinatorial proof of this formula by exhibiting a bijection between the set of unsorted Young Tableaux of shape A, and the set of pairs (T, S), where T is a Standard Young Tableau of sha...

A powerful extension of the tableau method is described. It consists in a new simpliication rule allowing to prune the search space and a new way of extracting a model from a given (possibly innnite) branch. These features are combined with a former method for simultaneous search for refutations and models. The possibilities of the new method w.r.t. the original one are clearly stated. In parti...

The structure of analytic signals is investigated by means of the relation between analytic signals and functions in the Hardy space. It is shown that an analytic signal is made up of two parts, one depends on the amplitude of the signal and another on the boundary value of an inner function. Based on this result, properties of the instantaneous frequencies of these two parts are studied, and i...

In [1] we studied a mixed-integer set arising from two rows of a simplex tableau. We showed that facets of such a set can be obtained from lattice point free triangles and quadrilaterals associated with either three or four variables. In this paper we generalize our findings and show that, when upper bounds on the non-basic variables are also considered, further classes of facets arise that can...

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 ...