Algebra for multivariate mappings over a finite set
Sprache des Vortragstitels:
AAA98 - 98th Workshop on General Algebra
Sprache des Tagungstitel:
We investigate multiple input output gates on a finite set. We investigate closure under serial and parallel composition, and demand that "wire permutations" are in our closed sets. We aim to use the tools similar to those of clone theory to investigate these closed sets. We are primarily interested in mappings that are bijections.
We will describe a number of results about the structure of closed sets. For instance we show that for odd |A|, there is a finite generating set for all bijections, while for even |A| there is no finite generating set.