We prove a conjecture of [3] giving a closed form formula for the norm of the Jack polynomials in superspace with respect to a certain scalar product. The proof is mainly combinatorial and relies on the explicit expression in terms of admissible tableaux of the non-symmetric Jack polynomials. In the final step of the proof appears an identity on weighted sums of partitions that we demonstrate u...

Let P be the Gelfand–Tsetlin polytope defined by the skew shape λ/μ and weight w. In the case corresponding to a standard Young tableau, we completely characterize for which shapes λ/μ the polytope P is integral. Furthermore, we show that P is a compressed polytopewhenever it is integral and corresponds to a standard Young tableau.We conjecture that a similar property holds for arbitraryw, name...

The use of bottom-up generated lemmas is an appropriate method for achieving an eeective redundancy control mechanism for connection tableau search procedures as well as for reducing proof lengths. An unbounded use of lemmas, however, usually does not lead to improvements of the search process and can even complicate the search. In order to identify lemmas which are actually relevant for the pr...

We identify a general property of concrete domains that is sufficient for proving decidability of DLs equipped with them and GCIs. We show that some useful concrete domains, such as a temporal one based on the Allen relations and a spatial one based on the RCC-8 relations, have this property. Then, we present a tableau algorithm for reasoning in DLs equipped with such concrete domains.

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