6 papers
Gosper's and Ramanujan's infinite products and generalizations
Jean-Paul Allouche, John M. Campbell, Simon R. Holcombe +2
Gosper introduced many remarkable formulas involving infinite products. One such formula provides an evaluation of the product $$\prod_{n \geq 1} \frac{1}{e}\left(\frac{1}{3n} + 1\…
Subword enumeration up to stack-sorting equivalence
John M. Campbell, Narad Rampersad
Defant and Kravitz introduced generalizations of West's stack-sorting map from permutations to finite words. This raises questions as to how such generalizations could be appli…
Meta-automatic Sequences
John M. Campbell, Benoit Cloitre
Nested (or meta-Fibonacci) recurrences, such as the recurrence used to define Hofstadter's Q-sequence, along with the digit-based recurrences that underlie automatic sequences are…
Reduced complexities for sequences over finite alphabets
John M. Campbell, James Currie, Narad Rampersad
Letting denote a finite, nonempty word, let denote the word obtained from by replacing every subword of of the form for a given charac…
The reflection complexity of sequences over finite alphabets
Jean-Paul Allouche, John M. Campbell, Shuo Li +2
In combinatorics on words, the well-studied factor complexity function $ρ_{\infw{x}}$ of a sequence $\infw{x}$ over a finite alphabet counts, for every nonnegative integer , the…
A binary version of the Mahler-Popken complexity function
John M. Campbell
The (Mahler-Popken) complexity of a natural number is the smallest number of ones that can be used via combinations of multiplication and addition to express , wit…