Discrete Vector Models for Catalysis and Autocatalysis

Abstract

Based on Ruch's concept of diagram lattices formed by Young diagrams we investigated the possibility to transform incomparable diagrams into comparable ones by means of vector catalysis. Ruch's diagram lattices allow a very general description of comparing frequency distributions by their mixing-character as an order relation which is equivalent to majorisation in the mathematical theory of inequalities. Dealing with Young diagrams or vectors containing only integer components, respectively, vector catalysis is strongly related to entanglement catalysis in quantum informatics. In a very systematic way the diagram lattices of the partitions up to the number n=20 have been searched for incomparable pairs which can be catalysed. This concept opens the opportunity for regarding vector catalysis as a universal phenomenon which is not restricted to the quantum mechanical idea of entanglement catalysis. Such a general approach offers the possibility to compare vector catalysis with chemical ideas of catalysis and autocatalysis in a very fundamental sense. We emphasize that vector catalysis is a universally valid procedure for classification purposes, where incomparable sequences of symbols are transformed into comparable ones in a much higher dimensional space ignoring any physical interpretation of these symbols.