Root-Patterns to Algebrising Partitions

DOI: 10.4236/apm.2015.51004   PDF   HTML   XML   2,037 Downloads   2,354 Views  

Abstract

The study of the confluences of the roots of a given set of polynomials—root-pattern problem— does not appear to have been considered. We examine the situation, which leads us on to Young tableaux and tableaux representations. This in turn is found to be an aspect of multipartite partitions. We discover, and show, that partitions can be expressed algebraically and can be “differentiated” and “integrated”. We show a complete set of bipartite and tripartite partitions, indicating equivalences for the root-pattern problem, for select pairs and triples. Tables enumerating the number of bipartite and tripartite partitions, for small pairs and triples are given in an appendix.

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Agacy, R. (2015) Root-Patterns to Algebrising Partitions. Advances in Pure Mathematics, 5, 31-41. doi: 10.4236/apm.2015.51004.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Agacy, R.L. and Briggs, J.R. (1994) Algebraic Classification of the Lanczos Tensor by Means of Its (3,1) Spinor Equivalent. Tensor, 55, 223-234.
[2] Agacy, R.L. (2002) Spinor Factorizations for Relativity. General Relativity and Gravitation, 34, 1617-1624.
http://dx.doi.org/10.1023/A:1020116122418
[3] Andrews, G.E. (1984) The Theory of Partitions. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511608650

  
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