This paper introduces MetTeL2, a tableau prover generator producing Java code from the specification of a logical syntax and a tableau calculus. It is intended to provide an easy to use system for non-technical users and allow technical users to extend the generated implementations.

This paper discusses a new strategy to decide Dummett logic. The strategy relies on a tableau calculus whose distinguishing features are the rules for implicative formulas. The strategy has been implemented and the experimental results are reported.

Let λ be a partition, and denote by f λ the number of standard tableaux of shape λ. The asymptotic shape of λ maximizing f λ was determined in the classical work of Logan and Shepp and, independently, of Vershik and Kerov. The analogue problem, where the number of parts of λ is bounded by a fixed number, was done by Askey and Regev – though some steps in this work were assumed without a proof. ...

tableau for that formula. The test generally does not terminate, but it does if a given formula is bisimulation invariant, i.e., the test is positive.

Nakajima introduced a certain set of monomials characterizing the irreducible highest weight crystals B(λ). The monomial set can be extended so that it contains B(∞) in addition to B(λ). We give explicit new realizations of the crystals B(∞) and B(λ) over special linear Lie algebras in the language of extended Nakajima monomials. Also, we introduce Young tableau realization of the crystal B(∞) ...

We give an account of the construction of exterior differential systems based on the notion of tableaux over Lie algebras as developed in [33]. The definition of a tableau over a Lie algebra is revisited and extended in the light of the formalism of the Spencer cohomology; the question of involutiveness for the associated systems and their prolongations is addressed; examples are discussed.

The Schur function indexed by a partition λ with at most n parts is the sum of the weight monomials for the Young tableaux of shape λ. Let π be an npermutation. We give two descriptions of the tableaux that contribute their monomials to the key polynomial indexed by π and λ. (These polynomials are the characters of the Demazure modules for GL(n).) The “atom” indexed by π is the sum of weight mo...

X iv :0 80 3. 22 53 v2 [ m at h. C O ] 4 F eb 2 00 9 DIAGONAL VECTORS OF SHIFTED YOUNG TABLEAUX DORIAN CROITORU Abstra t. We study ve tors formed by entries on the diagonal of standard Young tableaux of shifted shapes. Su h ve tors are in bije tion with integer latti e points of ertain integral polytopes, whi h are Minkowski sums of simpli es. We also des ribe verti es of these polytopes, and o...