Hyper $b$-ary expansions and Stern polynomials

Hyper $b$-ary expansions and Stern polynomials

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 charact...

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Hauptverfasser: Wakhare, Tanay, Kendrick, Caleb, Chung, Matthew, Cassell, Catherine, Santini, Stefano, Mosley, William Colin, Raghu, Anand, Morrison, Robert, Schurman, Iman, Beal, Timothy Kevin, Patrick, Matthew
Format: Artikel
Sprache:eng
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Mathematics - Combinatorics
Mathematics - Number Theory
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Zusammenfassung: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 $b$.
DOI:10.48550/arxiv.1810.11096