Reconstruction Problems for Graphs, Krawtchouk Polynomials, and Diophantine Equations

Chapter

Abstract

We give an overview about some reconstruction problems in graph theory, which are intimately related to integer roots of Krawtchouk polynomials. In this context, Tichy and the author recently showed that a binary Diophantine equation for Krawtchouk polynomials only has finitely many integral solution. Here, this result is extended. By using a method of Krasikov, we decide the general finiteness problem for binary Krawtchouk polynomials within certain ranges of the parameters.

Keywords

Krawtchouk polynomials Graph reconstruction Diophantine equations Discrete orthogonal polynomials Laguerre inequality 

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Notes

Acknowledgments

The author is a recipient of an APART-fellowship of the Austrian Academy of Sciences at the University of Waterloo, Canada. He also wishes to express his gratitude to I. Krasikov for several helpful discussions.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics, School of Computer ScienceUniversity of WaterlooWaterlooCanada

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