A note on some representations of SL(V)

A Note on Representations of Inverse Semigroups

It is known [l; 2] that every inverse semigroup 5 has a faithful representation as a semigroup of (1, l)-mappings of subsets of a set A into A. The set A may be taken as the set of elements of 5 and the (1, l)-mappings as mappings of principal left ideals of 5 onto principal left ideals of 5. If £ is the set of idempotents of 5 then there is also a representation of 5, not necessarily faithful,...

A Note on Cocycles of Unitary Representations

Given a unitary representation U of a locally compact abelian group G, we investigate the relationship between two cocycles a,, a2: Vax = a2+ b for some unitary operator V commuting with U and some coboundary b. A necessary and sufficient condition is given in terms of canonical-finite measures defined on G 1. These results are applied to the representation of Z defined by the shift of a statio...

A Note on Succinct Representations of Graphs

A note on models for graph representations

This paper is intended more to ask questions than to give answers. Specifically, we consider models for labeling schemes, and discuss issues regarding the number of labels consulted vs. the sizes of the labels. Recently, quite a few papers studied methods for representing network properties by assigning informative labels to the vertices of a network. Consider some graph function f on pairs of ...

A Note on Crossover with Interval Representations

We analyse crossover in Learning Classifier Systems with three different interval representations, using both niche and panmictic Genetic Algorithms. We find that the choice of interval representation has a significant bearing on the characteristics of offspring interval produced and the means by which evolutionary search is carried out.