Ernst-Christoph Haß, Sonja Sauerbrei and Peter Jörg Plath

Hindawi Publishing Corporation
Discrete Dynamics in Nature and Society
Volume 2008, Artikle ID 590142, 26 pages
doi: 10.1155 / 2008 / 590142

Based on Rush's concept of diagram lattices formed by Young diagrams we investigated the possibility to transform incomarable 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-characters as an order relation which is equivalent to majorisation in the mathematical theory of inequalities. Dealing with Young diagrams or vector containing only integer componets, respectively, vector catalysis is strongly related to entanglement catalysis in quantum informatics. In a very systematic way the diagram lattics of the partititions 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.

Copyright © 2008 Ernst-Christoph Hass et al. This is an open access article ditributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.