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Title: Guessing with little data

Speaker: Manuel Kauers Affiliation: Johannes Kepler University Zoom: Please email Emma Watson

Abstract:

A popular and powerful technique in experimental mathematics takes as input the first few terms of an infinite sequence and returns plausible candidates for recurrence equations that the sequence may satisfy. In a way, the search for such candidates is a generalization of polynomial interpolation. For polynomial interpolation, it is well known and easy to see that d+1 sample points are needed in order to recover a polynomial of degree d. Similarly, it turns out that (r+1)*(d+2) consecutive terms of a sequence are needed in order to detect a linear recurrence of order r with polynomial coefficients of degree at most d.