The point of view of the book derives from Leopold Kronecker (1823-1891), whose views were quite consonant with those of MAP. Kronecker resisted the overthrow of the Aristotelian (and Gaussian) prohibition of completed infinites on the ground that the overthrow was unnecessary. In other words, he committed himself to doing mathematics without completed infinites, basing his work on algorithmic ...

Kronecker-based approaches have been proposed for the solution of structured GSPNs with extremely large state spaces. Representing the transition rate matrix using Kronecker sums and products of smaller matrices virtually eliminates its storage requirements, but introduces various sources of overhead. We show how, by using a new data structure which we call matrix diagrams, we are able to great...

Indefinite summation, together with a generalized version of the Kronecker delta, provide a calculus for reasoning about various polynomial functions that arise in combinatorics, such as the Tutte, chromatic, flow, and reliability polynomials. In this paper we develop the algebraic properties of the indefinite summation operator and the generalized Kronecker delta from an axiomatic viewpoint. O...

Two new fixed polarity linear Kronecker transforms executed over GF(3) are introduced in this article. Both transforms are based on recursive equations using Kronecker products what allows to obtain simple corresponding fast transforms and very regular butterfly diagrams. The computational costs to calculate the new pair of transforms and their experimental comparison with ternary Reed–Muller t...

Let n ∈ N, 0 < α, β, γ < 1. Define the random Kronecker graph K(n, α, γ, β) to be the graph with vertex set Z2 , where the probability that u is adjacent to v is given by pu,v = α u·vγ(1−u)·(1−v)βn−u·v−(1−u)·(1−v). This model has been shown to obey several useful properties of real-world networks. We establish the asymptotic size of the giant component in the random Kronecker graph.

Abstract. We deduce using the Ringel-Hall algebra approach explicit formulas for the cardinalities of some Grassmannians over a finite field associated to the Kronecker quiver. We realize in this way a quantification of the formulas obtained by Caldero and Zelevinsky for the Euler characteristics of these Grassmannians. We also present a recursive algorithm for computing the cardinality of ever...

We show that the Kronecker coefficients indexed by two two-row shapes are given by quadratic quasipolynomial formulas whose domains are the maximal cells of a fan. Simple calculations provide explicitly the quasipolynomial formulas and a description of the associated fan. As an application, we characterize all the Kronecker coefficients indexed by two two-row shapes that are equal to zero. Join...

We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L2-norm of Ricci curvature for all complex surfaces of general type. We are also able to show that the standard metric on any complex hyperbolic 4manif...