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Largest values of the Stern sequence, alternating binary expansions and continuants

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Speaker: 
Roland Paulin
Affiliation: 
U of Salzburg/MPIM
Date: 
Wed, 07/09/2016 - 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

We study the largest values of the $r$th row of Stern's diatomic array.  In particular, we
prove some conjectures of Lansing.
Our main tool is the connection between the Stern
sequence, alternating binary expansions and continuants. This allows us to reduce the
problem of ordering the elements of the Stern sequence to the problem of ordering continuants.
We describe an operation that increases the value of a continuant, allowing us to reduce
the problem of largest continuants to ordering continuants of very special shape.
Finally, we order these special continuants using some identities and inequalities

involving Fibonacci numbers.
 

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