Uusi opinto-opas (sisältäen myös opetusohjelmat) lukuvuodelle 2018-2019 sijaitsee osoitteessa https://opas.peppi.utu.fi . Tältä sivustolta löytyvät enää vanhat opinto-oppaat ja opetusohjelmat.

The new study guide (incl. teaching schedules) for academic year 2018-2019 can be found at https://studyguide.utu.fi. This site contains only previous years' guides.

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Arkistoitu opetussuunnitelma 2014–2016
Selaamasi opetussuunnitelma ei ole enää voimassa. Tarkista tiedot voimassa olevasta opetussuunnitelmasta.
MATE5075 Combinatorics on Words 10 op
Organised by
Person in charge
Matematiikan ja tilastotieteen laitos, Juhani Karhumäki
Planned organizing times
Period(s) I II III IV
2015–2016 X X
Preceding studies
Basics on algorithms and combinatorics are needed, and on automata is useful.

Learning outcomes

To learn and get excited on simply formulated problems and results on sequences of elements, as well as to see connections of this topic to numerous areas of sciences, not only in mathematical sciences.


A word is a finite or infinite sequence of symbols (from a finite set). In this course we consider simple, as well as more advanced, combinatorial problems of words. For example, when two words commute, or how long words exist without containing a repetition of a certain type (like a square). Also some more algebraic properties of words are considered, results have applications in many fields of discrete mathematics and theoretical computer science.

Teaching methods

Teaching method Contact Online
Lectures 56 h 0 h
Exercises 26 h 0 h

Teaching language


Modes of study

Option 1
Available for:
  • Degree Programme Students
  • Other Students
  • Doctoral Students
  • Exchange Students
Exercises Exercise(s)
  • In English
Written exam
  • In English


Numeric 0-5.

Study materials

Lecture notes; M.Lothaire: Combinatorics on words, Addison-Wesley, 1983; C. Choffrut and J. Karhumäki: Combinatorics of words, in Handbook of Formal Languages Vol. 1 (G. Rozenberg and A. Salomaa, Eds.), pp. 329-438. Springer, Berlin 1997; M. Lothaire: Algebraic Combinatorics on Words (Encyclopedia of Mathematics and its Applications, vol. 90).Cambridge University Press 2002.

Belongs to following study modules

Matematiikan ja tilastotieteen laitos
Archived Teaching Schedule. Please refer to current Teaching Shedule.
Implementation details are unavailable.
Matematiikan ja tilastotieteen laitos