1 citations · 1 across the 11 of their papers we have counts for
16 papers
Algebraic Structures on Sets of Partitions
Madeline L. Dawsey, Megan du Preez, Rachel Van Surksum
Motivated by Robert Schneider's trailblazing work toward developing a unifying algebraic theory of integer partitions, we explore various binary operations on partitions to identif…
Non-standard Zeckendorf decompositions; or, Tribonacci within Fibonacci
Katie Anders, Madeline L. Dawsey, Joseph Vandehey
We study , the number of ways of writing as a sum or difference of the first Fibonacci numbers. We show that satisfies the Tribonacci-like recurrence $B(0;…
Non-standard quaternary representations and the Fibonacci numbers
Katie Anders, Madeline L. Dawsey, Rajat Gupta +2
Let be the number of hyperquaternary representations of and be the number of balanced quaternary representations of . We show that there is no integer …
Partition-theoretic model of prime distribution
Aidan Botkin, Madeline L. Dawsey, David J. Hemmer +2
We make an application of ideas from partition theory to a problem in multiplicative number theory. We propose a deterministic model of prime number distribution, from first princi…
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…
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…
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…
Self-conjugate -core partitions and applications
Madeline Locus Dawsey, Benjamin Sharp
Partition theory abounds with bijections between different types of partitions. One of the most famous partition bijections maps each self-conjugate partition of a positive integer…
Derivatives and Integrals of Polynomials Associated with Integer Partitions
Madeline Locus Dawsey, Tyler Russell, Dannie Urban
Integer partitions express the different ways that a positive integer may be written as a sum of positive integers. Here we explore the analytic properties of a new polynomial $f_λ…
Hypergeometric Functions over Finite Fields and Modular Forms: A Survey and New Conjectures
Madeline Locus Dawsey, Dermot McCarthy
Hypergeometric functions over finite fields were introduced by Greene in the 1980s as a finite field analogue of classical hypergeometric series. These functions, and their general…
Generalized Paley graphs and their complete subgraphs of orders three and four
Madeline Locus Dawsey, Dermot McCarthy
Let be an integer. Let be a prime power such that if is even, or, if is odd. The generalized Paley graph of or…
Fields generated by characters of finite linear groups
Madeline Locus Dawsey, Ken Ono, Ian Wagner
In previous work, the authors confirmed the speculation of J. G. Thompson that certain multiquadratic fields are generated by specified character values of sufficiently large alter…
Higher Width Moonshine
Madeline Locus Dawsey, Ken Ono
\textit{Weak moonshine} for a finite group is the phenomenon where an infinite dimensional graded -module has the property that its tra…
CM Evaluations of the Goswami-Sun Series
Madeline Locus Dawsey, Ken Ono
In recent work, Sun constructed two -series, and he showed that their limits as give new derivations of the Riemann-zeta values and . G…
Effective Bounds for the Andrews spt-function
Madeline Locus Dawsey, Riad Masri
In this paper, we establish an asymptotic formula with an effective bound on the error term for the Andrews smallest parts function . We use this formula to prove…
A new formula for Chebotarev densities
Madeline Locus Dawsey
We give a new formula for the Chebotarev densities of Frobenius elements in Galois groups. This formula is given in terms of smallest prime factors of integer…