We study the realizability over R of representations of the group U(n) of upper-triangular n× n matrices over F2. We prove that all the representations of U(n) are realizable over R if n ≤ 12, but that if n ≥ 13, U(n) has representations not realizable over R. This theorem is a variation on a result that can be obtained by combining work of J. Arregi and A. Vera-López and of the authors, but th...

Point configurations and convex polytopes play central roles in computational geometry and discrete geometry. For many problems, their combinatorial structures, i.e., the underlying oriented matroids up to isomorphism, are often more important than their metric structures. For example, the convexity, the face lattice of the convex hull and all possible triangulations of a given point configurat...

A classical link in 3-space can be represented by a Gauss phrase encoding a plane diagram of the link in a purely combinatorial way. A Gauss phrase may give rise not to a classical link, but to a diagram with virtual crossings. We describe a linear algorithm determining whether a Gauss phrase encodes a classical link. We characterize Wirtinger presentations realizable by virtual link groups.

Digital lters where unit delays are replaced with frequencydependent delays, such as rst order allpass sections, are often called warped lters since they implement lter specications on a warped non-uniform frequency scale. Warped IIR (WIIR) lters cannot be realized directly due to delayfree loops. Speci c solutions have been known that make WIIR lters realizable but no general approach has been...

A cryptographic primitive or a security mechanism can be specified in a variety of ways, such as a condition involving a game against an attacker, construction of an ideal functionality, or a list of properties that must hold in the face of attack. One reason that an ideal functionality is appealing is that if an implementation cannot be distinguished from an ideal functionality, by any feasibl...