8 citations · 39 across the 23 of their papers we have counts for
35 papers
A geometric proof of Lagrange's theorem for continued fractions
Anton Lukyanenko, Joseph Vandehey
For regular continued fractions (CFs), points with finite expansions are exactly the rationals and, by Lagrange's theorem, points with eventually-periodic expansions are exactly th…
On the th smallest part of a partition into distinct parts
Rajat Gupta, Noah Lebowitz-Lockard, Joseph Vandehey
A classic theorem of Uchimura states that the difference between the sum of the smallest parts of the partitions of into an odd number of distinct parts and the corresponding s…
On the number of partitions of a number into distinct divisors
Noah Lebowitz-Lockard, Joseph Vandehey
Let be the number of partitions of into distinct squarefree divisors of . In this note, we find a lower bound for , as well as a…
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…
Serendipitous decompositions of higher-dimensional continued fractions
Anton Lukyanenko, Joseph Vandehey
We prove a suite of dynamical results, including exactness of the transformation and piecewise-analyticity of the invariant measure, for a family of continued fraction systems, inc…
Convergence of improper Iwasawa Continued Fractions
Anton Lukyanenko, Joseph Vandehey
We prove the convergence of a wide class of continued fractions, including generalized continued fractions over quaternions and octonions. Fractional points in these systems are no…