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

Hyper $b$-ary expansions and Stern polynomials

Combinatorics 2018-10-29 v1 Number Theory

Authors: 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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@article{arxiv.1810.11096,
  title  = {Hyper $b$-ary expansions and Stern polynomials},
  author = {Tanay Wakhare and Caleb Kendrick and Matthew Chung and Catherine Cassell and Stefano Santini and William Colin Mosley and Anand Raghu and Robert Morrison and Iman Schurman and Timothy Kevin Beal and Matthew Patrick},
  journal= {arXiv preprint arXiv:1810.11096},
  year   = {2018}
}

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9 pages

Hyper $b$-ary expansions and Stern polynomials

Abstract

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