20 citations · 86 across the 50 of their papers we have counts for
56 papers
An example of an automatic sequence with non-regular abelian complexity
Jean-Paul Allouche, Narad Rampersad, Michel Rigo +2
Answering a question of Madill and Rampersad, we give an example a of a -automatic sequence whose abelian complexity is not -regular.
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\…
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 {…
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…
Repetition Threshold for Binary Automatic Sequences
J. -P. Allouche, N. Rampersad, J. Shallit
The critical exponent of an infinite word is the supremum, over all finite nonempty factors , of the exponent of . In this note we show that for all integers $k\geq 2…
Opacity complexity of automatic sequences. The general case
J. -P. Allouche, J. -Y. Yao
In this work we introduce a new notion called opacity complexity to measure the complexity of automatic sequences. We study basic properties of this notion, and exhibit an algorith…