In this paper we present a comparison of the service disciplines in real-time queueing systems (the customers have a deadline before which they should enter the service booth). We state that the more a service discipline gives priority to customers having an early deadline, the least the average stationary lateness is. We show this result by comparing adequate random vectors with the Schur-Conv...

In this paper, using a relation between Schur multipliers of pairs and triples of groups, the fundamental group and homology groups of a homotopy pushout of Eilenberg-MacLane spaces, we present among other things some behaviors of Schur multipliers of pairs and triples with respect to free, amalgamated free, and direct products and also direct limits of groups with topological approach.

The Pieri rule expresses the product of a Schur function and a single row Schur function in terms of Schur functions. We extend the classical Pieri rule by expressing the product of a skew Schur function and a single row Schur function in terms of skew Schur functions. Like the classical rule, our rule involves simple additions of boxes to the original skew shape. Our proof is purely combinator...

In this paper, we consider the boundedness of the Libera operator on Dirichlet spaces in terms of the Schur test. Moreover, we get its point spectrum and norm.

Recent work of A. Postnikov shows that cylindric skew Schur functions, which are a generalisation of skew Schur functions, have a strong connection with a problem of considerable current interest: that of finding a combinatorial proof of the non-negativity of the 3-point Gromov-Witten invariants. After explaining this motivation, we study cylindric skew Schur functions from the point of view of...

By the properties of Schur-convex function, Schur geometrically convex function and Schur harmonically convex function, Schur-convexity, Schur geometric and Schur harmonic convexities of the dual form for a class of symmetric functions are simply proved. As an application, several inequalities are obtained, some of which extend the known ones. Mathematics subject classification (2010): 26D15, 0...

An important problem in algebraic combinatorics is finding expansions of products of symmetric functions as sums of symmetric functions. Schur functions form a well-known basis for the ring of symmetric functions. The Littlewood-Richardson rule was introduced to expand the product of two Schur functions as a positive sum of Schur functions. Remmel and Whitney introduced an algorithmic way to fi...

In this paper, using the properties of Schur-convex function, Schur-geometrically convex function and Schur-harmonically convex function, we provide much simpler proofs of the Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a composite function of the complete symmetric function.

We introduce a quasisymmetric generalization of Berele and Regev’s hook Schur functions and prove that these new quasisymmetric hook Schur functions decompose the hook Schur functions in a natural way. In this paper we examine the combinatorics of the quasisymmetric hook Schur functions, providing analogues of the RobinsonSchensted-Knuth algorithm and a generalized Cauchy Identity. Résumé. Nous...