42 citations · 53 across the 11 of their papers we have counts for
13 papers
On Zeckendorf-Niven numbers and arithmetic progressions
Kelly Lao, Steven J. Miller, Nicholas Rosa +4
A positive integer is Zeckendorf-Niven (respectively, Lucas-Niven) if it is divisible by the number of summands in its Zeckendorf decomposition (respectively, Lucas decomposition).…
Arithmetic progressions of integers that are relatively prime to their digital sums
Ryan Blau, Joshua Harrington, Sarah Lohrey +2
For an integer , we call a positive integer -anti-Niven if it is relatively prime to the sum of the digits in its base- representation. In this article, we investiga…
Every arithmetic progression contains infinitely many -Niven numbers
Joshua Harrington, Matthew Litman, Tony W. H. Wong
For an integer , a positive integer is called a -Niven number if it is a multiple of the sum of the digits in its base- representation. In this article, we show that…
Probabilistic chip-collecting games with modulo winning conditions
Joshua Harrington, Xuwen Hua, Xufei Liu +3
Let , , and be integers with . In a certain two-player probabilistic chip-collecting game, Alice tosses a coin to determine whether she collects chips or …
Covering systems with odd moduli
Joshua Harrington, Yewen Sun, Wing Hong Tony Wong
The concept of a covering system was first introduced by Erdős in 1950. Since their introduction, a lot of the research regarding covering systems has focused on the existence of c…
Residue sums of Dickson polynomials over finite fields
Thomas Brazelton, Joshua Harrington, Matthew Litman +1
Given a polynomial with integral coefficients, one can inquire about the possible residues it can take in its image modulo a prime . The sum over the distinct residues can somet…
On binomial coefficients associated with Sierpiński and Riesel numbers
Ashley Armbruster, Grace Barger, Sofya Bykova +5
In this paper, we investigate the existence of Sierpiński numbers and Riesel numbers as binomial coefficients. We show that for any odd positive integer , there exist infinitely…
On the properties of fibotomic polynomials
Cameron Byer, Tyler Dvorachek, Emily Eckard +3
Define the -th fibotomic polynomial to be the product of the monic irredicible factors of the -th Fibonacci polynomial which are not factors of any Fibonacci polynomial of sm…
Sum index and difference index of graphs
Joshua Harrington, Eugene Henninger-Voss, Kedjar Karhadkar +2
Let be a nonempty simple graph with a vertex set and an edge set . For every injective vertex labeling , there are two induced edge labelings,…
An Investigation on Partitions with Equal Products
Byungchul Cha, Adam Claman, Joshua Harrington +6
An ordered triple is called admissible if there exist two different multisets and such that and share the sa…
On the Domination Number of Permutation Graphs and an Application to Strong Fixed Points
Theresa Baren, Michael Cory, Mia Friedberg +6
A permutation graph is a simple graph with vertices corresponding to the elements of and an edge between and when and are inverted in . A set of vertic…
Integrality of relative BPS state counts of toric Del Pezzo surfaces
Michel van Garrel, Tony W. H. Wong, Gjergji Zaimi
Relative BPS state counts for log Calabi-Yau surface pairs were introduced by Gross-Pandharipande-Siebert and conjectured by the authors to be integers. For toric Del Pezzo surface…
Algebraic techniques in designing quantum synchronizable codes
Yuichiro Fujiwara, Vladimir D. Tonchev, Tony W. H. Wong
Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously kno…