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...

n-tableaux [1] and δ-resolution [2], which are based, respectively, on semantic tableaux and resolution, have been properly used for the resolution of abductive problems. The tool we present is a Prolog implementation of an abductive solver which combines both calculi to attack first order abductive problems by reducing them to finite versions, that is, propositional rewritings of the problems ...

This paper establishes the decidability of SR⊔IQ which has composition-based role Inclusion axioms (RIAs) of the form R1 ◦ · · · ◦ Rn⊑̇T1 ⊔ · · · ⊔ Tm. Also the consistency of an Abox A of SR⊔IQ DL w.r.t. Rbox R is established. Motivation for this kind of RIAs comes from applications in the field of manufactured products as well as other conceptual modeling applications such as family relationsh...

This article uses combinatorial objects called labeled abaci to give direct combinatorial proofs of many familiar facts about Schur polynomials. We use abaci to prove the Pieri rules, the Littlewood–Richardson rule, the equivalence of the tableau definition and the determinant definition of Schur polynomials, and the combinatorial interpretation of the inverse Kostka matrix (first given by Eğec...

Following the approach [Schwind, Risch, 91] to Reiter’s default logic, tiffs paper attempts to define a general tableaux-based framework for tt~c cornlmtation of tile extensions for several known default k)gics. The idea is to qualify the differences b(;twecn the wlriants under considcration inside a single process that can switcil easily from one variant to another. Indeed, the approach is rel...