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arXiv · 1810.11096

Hyper $b$-ary expansions and Stern polynomials

Tanay Wakhare·Caleb Kendrick·Matthew Chung·Catherine Cassell·Stefano Santini·William Colin Mosley·Anand Raghu·Robert Morrison·Iman Schurman·Timothy Kevin Beal·Matthew Patrick
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Abstract

We study a recently introduced base $b$ polynomial analog of Stern's diatomic sequence, which generalizes Stern polynomials of Klavar, Dilcher, Ericksen, Mansour, Stolarsky, and others. We lift some basic properties of base $2$ Stern polynomials to arbitrary base, and introduce a matrix characterization of Stern polynomials. By specializing, we recover some new number theoretic results about hyper $b$-ary partitions, which count partitions of $n$ into powers of $b$.

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Tanay Wakhare, Caleb Kendrick, Matthew Chung, Catherine Cassell, Stefano Santini, William Colin Mosley, Anand Raghu, Robert Morrison, Iman Schurman, Timothy Kevin Beal, Matthew Patrick. 2018-10-25. Hyper $b$-ary expansions and Stern polynomials. https://arxiv.org/abs/1810.11096

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