J. Shallit

activity

20002025

most citedWords avoiding reversed subwords

15 citations · 105 across the 67 of their papers we have counts for

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Showing 2021Show all

6 papers · 1 filter

math.CO2021

Congruence properties of combinatorial sequences via Walnut and the Rowland-Yassawi-Zeilberger automaton

Narad Rampersad, Jeffrey Shallit

Certain famous combinatorial sequences, such as the Catalan numbers and the Motzkin numbers, when taken modulo a prime power, can be computed by finite automata. Many theorems abou…

cs.FL2021

Automatic Sequences of Rank Two

Jason Bell, Jeffrey Shallit

Given a right-infinite word $x$ over a finite alphabet $A$ , the rank of $x$ is the size of the smallest set $S$ of words over $A$ such that $x$ can be realized as an in…

cs.DM2021

Mesosome Avoidance

Robert Cummings, Jeffrey Shallit, Paul Staadecker

We consider avoiding mesosomes -- that is, words of the form $x x^{'}$ with $x^{'}$ a conjugate of $x$ that is different from $x$ -- over a binary alphabet. We give a structure theorem fo…

math.NT2021

How to prove that a sequence is not automatic

J. -P. Allouche, J. Shallit, R. Yassawi

Automatic sequences have many properties that other sequences (in particular, non-uniformly morphic sequences) do not necessarily share. In this paper we survey a number of differe…

math.NT2021

Frobenius Numbers and Automatic Sequences

Jeffrey Shallit

The Frobenius number $g (S)$ of a set $S$ of non-negative integers with $g cd 1$ is the largest integer not expressible as a linear combination of elements of $S$ . Given a sequence…

cs.FL2021

Lie complexity of words

Jason P. Bell, Jeffrey Shallit

Given a finite alphabet $Σ$ and a right-infinite word $w$ over $Σ$ , we define the Lie complexity function $L_{w} : N \to N$ , whose value at $n$ is the number…