127 citations · 1.2k across the 174 of their papers we have counts for
19 papers · 1 filter
Determining optimal test functions for -level densities
Elżbieta Bołdyriew, Fangu Chen, Charles Devlin VI +2
Katz and Sarnak conjectured a correspondence between the -level density statistics of zeros from families of -functions with eigenvalues from random matrix ensembles. In many…
Modeling Random Walks to Infinity on Primes in
Bencheng Li, Steven J. Miller, Tudor Popescu +2
An interesting question, known as the Gaussian moat problem, asks whether it is possible to walk to infinity on Gaussian primes with steps of bounded length. Our work examines a si…
Generalizing Ruth-Aaron Numbers
Yanan Jiang, Steven J. Miller
Let be the sum of the prime divisors of , counted with multiplicity; thus . Ruth-Aaron numbers, or integers with $f(n)=f(n…
Winning Strategy for the Multiplayer and Multialliance Zeckendorf Games
Anna Cusenza, Aidan Dunkelberg, Kate Huffman +7
Edouard Zeckendorf proved that every positive integer can be uniquely written \cite{Ze} as the sum of non-adjacent Fibonacci numbers, known as the Zeckendorf decomposition. Bas…
An Introduction to Completeness of Positive Linear Recurrence Sequences
Elżbieta Bołdyriew, John Haviland, Phúc Lâm +3
A positive linear recurrence sequence (PLRS) is a sequence defined by a homogeneous linear recurrence relation with positive coefficients and a particular set of initial conditions…
Walking to Infinity Along Some Number Theory sequences
Steven J. Miller, Fei Peng, Tudor Popescu +3
An interesting open conjecture asks whether it is possible to walk to infinity along primes, where each term in the sequence has one digit more than the previous. We present differ…
Completeness of Positive Linear Recurrence Sequences
Elżbieta Bołdyriew, John Haviland, Phúc Lâm +3
A sequence of positive integers is complete if every positive integer is a sum of distinct terms. A positive linear recurrence sequence (PLRS) is a sequence defined by a homogeneou…
Extending Zeckendorf's Theorem to a Non-constant Recurrence and the Zeckendorf Game on this Non-constant Recurrence Relation
Elżbieta Bołdyriew, Anna Cusenza, Linglong Dai +16
Zeckendorf's Theorem states that every positive integer can be uniquely represented as a sum of non-adjacent Fibonacci numbers, indexed from . This has been gene…
The limiting spectral measure for an ensemble of generalized checkerboard matrices
Fangu Chen, Jiahui Yu, Steven J. Miller +1
Random matrix theory successfully models many systems, from the energy levels of heavy nuclei to zeros of -functions. While most ensembles studied have continuous spectral distr…
Bounds on Zeckendorf Games
Anna Cusenza, Aiden Dunkelberg, Kate Huffman +7
Zeckendorf proved that every positive integer can be written uniquely as the sum of non-adjacent Fibonacci numbers. We use this decomposition to construct a two-player game. Gi…
Constructions of Generalized MSTD Sets in Higher Dimensions
Elena Kim, Steven J. Miller
Let be a set of finite integers, define and for non-negative integers and define $…
Tinkering with Lattices: A New Take on the Erdős Distance Problem
Elzbieta Boldyriew, Elena Kim, Steven J. Miller +4
The Erdős distance problem concerns the least number of distinct distances that can be determined by points in the plane. The integer lattice with points is known as \texti…
Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, II
Thomas C. Martinez, Steven J. Miller, Clayton Mizgerd +2
Zeckendorf's theorem states that every positive integer can be written uniquely as the sum of non-consecutive shifted Fibonacci numbers , where we take and …
Deterministic Zeckendorf Games
Ruoci Li, Xiaonan Li, Steven J. Miller +4
Zeckendorf proved that every positive integer can be written uniquely as the sum of non-adjacent Fibonacci numbers. We further explore a two-player Zeckendorf game introduced in Ba…
Zeckendorf's Theorem Using Indices in an Arithmetic Progression
Amelia Gilson, Hadley Killen, Tamás Lengyel +4
Zeckendorf's Theorem states that any positive integer can be uniquely decomposed into a sum of distinct, non-adjacent Fibonacci numbers. There are many generalizations, including r…
Generalizing the Distribution of Missing Sums in Sumsets
Hung V. Chu, Dylan King, Noah Luntzlara +5
Given a finite set of integers , its sumset is . We examine as a random variable, where , the set of integer…
On Zeckendorf Related Partitions Using the Lucas Sequence
Hung V. Chu, David C. Luo, Steven J. Miller
Zeckendorf proved that every positive integer has a unique partition as a sum of non-consecutive Fibonacci numbers. Similarly, every natural number can be partitioned into a sum of…
Distribution of missing differences in diffsets
Scott Harvey-Arnold, Steven J. Miller, Fei Peng
Lazarev, Miller and O'Bryant investigated the distribution of for chosen uniformly at random from , and proved the existence of a divot at missing…
Extensions of Autocorrelation Inequalities with Applications to Additive Combinatorics
Sara Fish, Dylan King, Steven J. Miller
In a 2019 paper, Barnard and Steinerberger show that for , the following autocorrelation inequality holds: \begin{equation*} \min_{0 \leq t \leq 1} \int_\math…