127 citations · 1.2k across the 174 of their papers we have counts for
10 papers · 1 filter
On the sum of -th powers in terms of earlier sums
Steven J. Miller, Enrique Treviño
For a positive integer let , i.e., is the sum of the first -th powers. Faulhaber conjectured (later proved by Jacobi) that for $k…
Recurrence Relations and Benford's Law
Madeleine Farris, Noah Luntzlara, Steven J. Miller +2
There are now many theoretical explanations for why Benford's law of digit bias surfaces in so many diverse fields and data sets. After briefly reviewing some of these, we discuss…
The Fibonacci Quilt Game
Steven J. Miller, Alexandra Newlon
Zeckendorf proved that every positive integer can be expressed as the sum of non-consecutive Fibonacci numbers. This theorem inspired a beautiful game, the Zeckendorf Game. Two pla…
Gaps of Summands of the Zeckendorf Lattice
Neelima Borade, Dexter Cai, David Z. Chang +4
A beautiful theorem of Zeckendorf states that every positive integer has a unique decomposition as a sum of non-adjacent Fibonacci numbers. Such decompositions exist more generally…
Crescent configurations in normed spaces
Sara Fish, Dylan King, Steven J. Miller +2
We study the problem of crescent configurations, posed by Erdős in 1989. A crescent configuration is a set of points in the plane such that: 1) no three points lie on a common…
Higher Order Fibonacci Sequences from Generalized Schreier sets
Hung Viet Chu, Steven J. Miller, Zimu Xiang
A Schreier set is a subset of the natural numbers with . It has been known that the sequence , where $$a_{1,n}\ :=\ |\{S\subseteq \mathbb{N}\,:\,\max…