4 citations · 4 across the 9 of their papers we have counts for
12 papers
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;…
Structural properties of graphs and the Universal Difference Property
Katie Anders, Able Martinez, Patrick McHugh +2
We study the Universal Difference Property (UDP) introduced by Altınok, Anders, Arreola, Asencio, Ireland, Sarıoğlan, and Smith, focusing on the relationship between the structural…
The wild number of an edge-colored graph
Katie Anders, Briana Foster-Greenwood, Rebecca Garcia +1
We introduce the wild number of an edge-colored graph as a measure of how close an edge-colored graph is to having a spanning tree in every color. This combinatorial concept origin…
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 …
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…