3 papers
math.CO2023
Non-standard binary representations and the Stern sequence
Katie Anders, Madeline Locus Dawsey, Rajat Gupta +1
We show that the number of short binary signed-digit representations of an integer is equal to the -th term in the Stern sequence. Various proofs are provided, including dir…
math.NT2023
Representations of integers as quotients of sums of distinct powers of three
Katie Anders, Madeline Locus Dawsey, Bruce Reznick +1
Which integers can be written as a quotient of sums of distinct powers of three? We outline our first steps toward an answer to this question, beginning with a necessary and almost…
math.CO2022
Bijections, generalizations, and other properties of sequentially congruent partitions
Ezekiel Cochran, Madeline Locus Dawsey, Emma Harrell +1
Recently, Schneider and Schneider defined a new class of partitions called sequentially congruent partitions, in which each part is congruent to the next part modulo its index, and…