This paper describes unimodular probing { a new technique that has been used to solve a class of dynamic scheduling problems. In benchmarks a unimodular probing algorithm has outperformed two well-established approaches: backtrack search with local consistency and spe-cialised heuristics, and mixed integer programming (MIP). The problems amenable to unimodular probing involve disjunctive constr...

We discuss sharpness in the Hausdorff Young theorem for unimodular groups. First the functions on unimodular locally compact groups for which equality holds in the Hausdorff Young theorem are determined. Then it is shown that the Hausdorff Young theorem is not sharp on any unimodular group which contains the real Une as a direct summand, or any unimodular group which contains an Abelian normal ...

We are mainly concerned with the completablity of unimodular rows to an invertible matrix. We first relate this to stable range of the ring. Further, we consider rows generating an idempotent of the ring to obtain completability under special conditions. We try to obtain analogues of important theorems regarding unimodular rows in the case of these “idempotent rows”. By ring, we shall always me...

Abstract. The class of systems of uniform recurrence equations (UREs) is closed under unimodular transformations. As a result, every systolic array described by a unimodular mapping can be specified by a system of space-time UREs, in which the time and space coordinates are made explicit. As non-unimodular mappings are frequently used in systolic designs, this paper presents a method that deriv...

By using Construction A modulo 4 the following remarkable unimodular lattices have been constructed: the Gosset lattice E8, the Leech lattice, the 23 Niemeier lattices in dimension 24, the two extremal even unimodular lattices in dimension 32 with an automorphism of order 31, all the extremal unimodular lattices and the odd Leech lattice. In this survey, we review basic facts of life in the Z4 ...

The purpose of this note is to announce results obtained in the analytic continuation of the (nondegenerate) "principal series" of representations of the nXn complex unimodular group. This study has as its starting point a similar one for the 2X2 real unimodular group previously carried out by us in [4]. We let G be the nXn complex unimodular group and C its diagonal subgroup consisting of elem...

A golden lattice is an even unimodular Z[ 1+ √ 5 2 ]-lattice of which the Hilbert theta series is an extremal Hilbert modular form. We construct golden lattices from extremal even unimodular lattices and obtain families of dense modular lattices.