Reconstruction Problems for Graphs, Krawtchouk Polynomials, and Diophantine Equations
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.
KeywordsKrawtchouk polynomials Graph reconstruction Diophantine equations Discrete orthogonal polynomials Laguerre inequality
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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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