Jeffrey Shallit

activity

20172025

most citedDecidability and k-Regular Sequences

2 citations · 3 across the 11 of their papers we have counts for

collaborators

Showing math.COShow all

5 papers · 1 filter

math.CO2025★ 1 cited

Runs in Paperfolding Sequences

Jeffrey Shallit

The paperfolding sequences form an uncountable class of infinite sequences over the alphabet ${- 1, 1}$ that describe the sequence of folds arising from iterated folding of a pi…

math.CO2025

Cloitre's Self-Generating Sequence

Jeffrey Shallit

In 2009 Benoit Cloitre introduced a certain self-generating sequence $(a_{n})_{n \geq 1} = 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, \dots,$ with the property that the sum of th…

math.CO2022

Some Tribonacci Conjectures

Jeffrey Shallit

In a recent talk of Robbert Fokkink, some conjectures related to the infinite Tribonacci word were stated by the speaker and the audience. In this note we show how to prove (or dis…

math.CO2022

Record-Setters in the Stern Sequence

Ali Keramatipour, Jeffrey Shallit

Stern's diatomic series, denoted by $(a (n))_{n \geq 0}$ , is defined by the recurrence relations $a (2 n) = a (n)$ and $a (2 n + 1) = a (n) + a (n + 1)$ for $n \geq 1$ , and initial values…

math.CO2017

Continuants, run lengths, and Barry's modified Pascal triangle

Jeffrey Shallit, Lukas Spiegelhofer

We show that the $n$ 'th diagonal sum of Barry's modified Pascal triangle can be described as the continuant of the run lengths of the binary representation of $n$ . We also obtain a…