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- Title
Generalization of the Harary-Palmer power group theorem to all irreducible representations of object and color groups- color combinatorial group theory.
- Authors
Balasubramanian, Krishnan
- Abstract
The Harary-Palmer classic power group enumeration theorem applies to a group G acting on a set D of objects such as vertices, edges, faces and simultaneously with a group H acting on another set R of colors such that the power group $$\hbox {H}^\mathrm{G}$$ acts on the set $$\hbox {R}^\mathrm{D}$$ of all functions from D to R. In this paper we show for the first time that the power group enumeration can be generalized to all irreducible representations of the object group G of D and also all irreducible representations of the color group H of R. We have also provided interpretation of various power group generating functions for different irreducible representations in the context of color symmetry group theory. Special cases of the power group enumeration with all irreducible representations of G keeping the color group representation fixed to the totally symmetric representation are shown to have important enumerative combinatorial applications in a number of problems of chemistry, physics and biology that involve color symmetry (color inversions) such as magnetism, neutron imaging, NMR, ESR spectroscopy, catalytic functions of non-rigid disordered proteins, and quantum chromodynamics of strong interactions of fundamental particles.
- Subjects
GROUP theory; SYMMETRY groups; COMBINATORIAL enumeration problems; MAGNETISM; COLOR symmetries (Particle physics); QUANTUM chromodynamics; NUCLEAR magnetic resonance spectroscopy
- Publication
Journal of Mathematical Chemistry, 2014, Vol 52, Issue 2, p703
- ISSN
0259-9791
- Publication type
Article
- DOI
10.1007/s10910-013-0290-0