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Polynomial Factorisation and an Application to Regular Directed Graphs

โœ Scribed by Stephen D. Cohen

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
441 KB
Volume
4
Category
Article
ISSN
1071-5797

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โœฆ Synopsis

The main theme is the distribution of polynomials of given degree which split into a product of linear factors over a finite field. The work was motivated by the following problem on regular directed graphs. Extending a notion of Chung, Katz has defined a regular directed graph based on the k-algebra k[X]/( f ), where k is the finite field of order q and f a monic polynomial of degree n over k. It is shown that the diameter of this graph is at most n#2 whenever q5B(n)"[n(n#2)!]. This improves on the work of Katz who gave a similar result for square-free polynomials f without specifying B(n).

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