论文信息 - Polynomial Factorisation and an Application to Regular Directed Graphs

Polynomial Factorisation and an Application to Regular Directed Graphs

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 thek-algebrakX]/(f), wherekis the finite field of orderqandfa monic polynomial of degreenoverk. It is shown that the diameter of this graph is at mostn+2 wheneverq?B(n)=n(n+2)!]2. This improves on the work of Katz who gave a similar result for square-free polynomialsfwithout specifyingB(n).

Stephen D. Cohen | Stephen D. Cohen

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