Lukas Spiegelhofer

activity

20152025

most citedNormality of the Thue--Morse sequence along Piatetski-Shapiro sequences, II

21 citations · 60 across the 22 of their papers we have counts for

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5 papers · 1 filter

math.CO2021

Gaps in the Thue--Morse word

Lukas Spiegelhofer

The Thue--Morse sequence is a prototypical automatic sequence found in diverse areas of mathematics, and in computer science. We study occurrences of factors $w$ within this sequen…

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…

math.CO2017

The Tu--Deng Conjecture holds almost surely

Lukas Spiegelhofer, Michael Wallner

The Tu--Deng Conjecture is concerned with the sum of digits $w (n)$ of $n$ in base~ $2$ (the Hamming weight of the binary expansion of $n$ ) and states the following: assume that $k$ …

math.CO2015

The maximal order of hyper-( $b$ -ary)-expansions

Michael Coons, Lukas Spiegelhofer

Using methods developed by Coons and Tyler, we give a new proof of a recent result of Defant, by determining the maximal order of the number of hyper-( $b$ -ary)-expansions of a nonn…

math.CO2015

On a Conjecture of Cusick Concerning the Sum of Digits of n and n + t

Michael Drmota, Manuel Kauers, Lukas Spiegelhofer

For a nonnegative integer $t$ , let $c_{t}$ be the asymptotic density of natural numbers $n$ for which $s (n + t) \geq s (n)$ , where $s (n)$ denotes the sum of digits of $n$ in base $2$ .…

Gaps in the Thue--Morse word

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

The Tu--Deng Conjecture holds almost surely

The maximal order of hyper-(b-ary)-expansions

On a Conjecture of Cusick Concerning the Sum of Digits of n and n + t

The maximal order of hyper-( $b$ -ary)-expansions