Year: 2024
Type: article
Abstract: We show that the number of short binary signed-digit representations of an integer $n$ is equal to the $n$-th term in the Stern sequence. Various proofs are provided, including direct, bijective, and generating function proofs. We also show that this result can be derived from recent work of Monroe on binary signed-digit representations of a fixed length.
DOI: 10.37236/12312
Authors: Katie Anders, Madeline Locus Dawsey, Rajat Gupta, Joseph Vandehey
Institutions: The University of Texas at Tyler, University of Maine
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404413616