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On the Dynamical Wilf-Zeilberger Problem

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Sun_Yuxuan.pdf (469.86 KB)

Date

2022-08-15

Authors

Sun, Yuxuan

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University of Waterloo

Abstract

In this paper, we give an algorithmic solution to a dynamical analog of the problem of certifying combinatorial identities by Wilf-Zeilberger pairs. Given two sequences generated in a dynamical setting, we calculate an upper bound N ≥ 1 such that whenever the first N terms of the two sequences agree pairwise, the two sequences agree term-by-term. Then, we give an algorithm that can be used to check whether two such sequences agree term-by-term. Our methods are mainly based on the theory of Chow rings of algebraic varieties.

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Keywords

algebraic geometry, intersection theory, Wilf-Zeilberger pairs, arithmetic dynamics, dynamically generated sequences, elliptic divisibility sequences

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http://hdl.handle.net/10012/18543

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Pure Mathematics