3 papers
math.CO2025
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 $Ï_{\infw{x}}$ of a sequence $\infw{x}$ over a finite alphabet counts, for every nonnegative integer , th…
math.NT2025
Doubling modulo odd integers, generalizations, and unexpected occurrences
Jean-Paul Allouche, Manon Stipulanti, Jia-Yan Yao
The starting point of this work is an equality between two quantities and found in the literature, which involve the {\em doubling-modulo-an-odd-integer} map, i.e., $x\in {…
math.CO2025
Combinatorics on words and generating Dirichlet series of automatic sequences
Jean-Paul Allouche, Jeffrey Shallit, Manon Stipulanti
Generating series are crucial in enumerative combinatorics, analytic combinatorics, and combinatorics on words. Though it might seem at first view that generating Dirichlet series…