 Hypersymmetric functions and Pochhammers of 2 × 2 nonautonomous matricesA. F. Antippa International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-20 Abstract: We introduce the hypersymmetric functions of 2 × 2 nonautonomous matrices and show that they are related, by simple expressions, to the Pochhammers (factorial polynomials) of these matrices. The hypersymmetric functions are generalizations of the associated elementary symmetric functions , and for a specific class of 2 × 2 matrices, having a high degree of symmetry, they reduce to these latter functions. This class of matrices includes rotations, Lorentz boosts, and discrete time generators for the harmonic oscillators. The hypersymmetric functions are defined over four sets of independent indeterminates using a triplet of interrelated binary partitions. We work out the algebra of this triplet of partitions and then make use of the results in order to simplify the expressions for the hypersymmetric functions for a special class of matrices. In addition to their obvious applications in matrix theory, in coupled difference equations, and in the theory of symmetric functions, the results obtained here also have useful applications in problems involving successive rotations, successive Lorentz transformations, discrete harmonic oscillators, and linear two-state systems. Date: 2004 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:328284 DOI: 10.1155/S016117120431210X Access Statistics for this article More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.