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Seminario Dr. Lama Tarsissi

26 Gennaio 2018 (Archiviata)

Synchronization of three Christoffel words.

Mercoledì 31 Gennaio 2018 alle ore 15:00 
Sala Conferenze "F. Tricerri" del Dipartimento di Matematica "U. Dini

Relatore:
Dr. Lama Tarsissi
Laboratoire I3S, Sophia Antipolis, Nice

Titolo:
Synchronization of three Christoffel words.

Abstract:
Christoffel words are fundamental objects in combinatorics which share
many geometric, algebraic and arithmetic properties. Among them and in
discrete geometry, Christoffel words are coding of a discrete segment on
a grid from (0, 0) to (a, b). Christoffel words have an algebraic
interpretation using Cayley graph and two generators g1 = a, g2 = b over
Z/nZ, with n = a + b. In addition to that many algorithms in discrete
geometry and computer imagery deal with plotting segments on a computer
screen and thus Christoffel words are also a fundamental object for this
topic.
In parallel, many computer scientists work on synchronization of
processors and try to design optimal algorithms in order to balance the
charge between more than two servers. This optimal solution for the case
with two servers is given either by aperiodic balanced words namely the
Sturmian words or by periodic balanced words namely Christoffel words
repeated periodically.
For three servers and more, the problem is more complicated and leads to
the study of balanced words on a three letters alphabet or more. In this
presentation, I will introduce a new tool that allows us to study the
synchronization of three Christoffel words.

 

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