In this paper we compare the numerical properties of the well-known fast O(n 2) Traub and Bjj orck-Pereyra algorithms, which both use the special structure of a Vandermonde matrix to rapidly compute the entries of its inverse. The results of numerical experiments suggest that the Parker variant of what we shall call the Parker-Traub algorithm allows one not only fast O(n 2) inversion of a Vande...

We study convergent (terminating and confluent) presentations of n-categories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalising the one introduced by Squier for word rewriting systems. We characterise this property by using the notion of critical branching. In particular, we define sufficient conditions f...

Constraint Handling Rules (CHRs) are a powerful rule based language for specifying constraint solvers. Critical for any rule based language is the notion of confluence, and for terminating CHRs there is a decidable test for confluence. But many CHR programs that in practice are confluent fail this confluence test. The problem is that the states that illustrate non-confluence are not reachable i...

Our goal is to give a list of rewriting properties, and then automatically find a term rewriting system (TRS) satisfying these properties. In earlier work we did this for finite abstract reduction systems; in this paper we extend the approach to ground term rewriting systems over constants and one unary symbol. In particular, we fully automatically find a TRS that is locally confluent but not c...

Using the basic fact that any formal power series over the real or complex number field can always be expressed in terms of given polynomials {pn(t)}, where pn(t) is of degree n, we extend the ordinary Riordan array (resp. Riordan group) to a generalized Riordan array (resp. generalized Riordan group) associated with {pn(t)}. As new application of the latter, a rather general Vandermonde-type c...

In this paper, we establish several properties of the unified generalized Stirling numbers of the first kind, and the Jacobi-Stirling numbers of the first kind, by means of the convolution principle of sequences. Obtained results include generalized Vandermonde convolution for the unified generalized Stirling numbers of the first kind, triangular recurrence relation for general Stirling-type nu...

Given a constructor term rewriting system defining injective functions, the inversion compiler proposed by Nishida, Sakai and Sakabe generates a confluent conditional term rewriting system, and unravels the conditional system into an unconditional term rewriting system. In general, the unconditional system is not confluent and thus not computationally equivalent to the conditional system. In th...

We construct confluent supersymmetric partners of quantum systems that emerge from the spheroidal equation. Properties of the systems and of their transformed counterparts are discussed.

We rst review the basic properties of the well known classes of Toeplitz Hankel Vandermonde and other related structured matrices and re examine their correlation to operations with univariate polynomials Then we de ne some natural extensions of such classes of matrices based on their correlation to multivariate polynomials We describe the correlation in terms of the associated operators of mul...