Enumerative combinatorics and applications of this field of mathematics to computer science was the theme of a two-week long CIMPA School hosted by Stellenbosch 肆客足球's (SU) Department of Mathematical Sciences.
CIMPA is the acronym for the French non-profit organization, the Centre International de Mathématiques Pures et Appliquées (CIMPA), founded in 1978 to promote research in Mathematics in developing countries. CIMPA supports about 20 such schools every year.
Dr Sarah Selkirk, member of the scientific committee and an SU alumnus, says the aim of the school is “to grow the network of enumerative combinatorics researchers within Africa and to increase participation of these researchers within the international research community". Selkirk is currently a research fellow at the 肆客足球 of Warwick in the United Kingdom.
Enumerative combinatorics is about counting mathematical objects. Selkirk explains: “Given five people and five chairs, in how many ways can we arrange the five people into the chairs? In this case there are 120 ways, which can be checked with simple counting arguments. As counting problems become more complex, more powerful methods, such as generating functions, are required. These counting methods can be used to analyse how much time it would take an algorithm to run – a topic that was covered during the school."
During the two weeks the 35 postgraduate students from 15 different African countries were introduced to topics such as Enumeration methods; Introduction to Analytic Combinatorics; Partitions and q-series; Tree enumeration and tree parameters; Permutation statistics; Analysis of algorithms; and using SageMath to generate combinatorial objects and experimental combinatorics, as well as packages for guessing generating functions and performing asymptotic expansions.
Attention was also given to the professional development of the participants. This included a workshop on having an online presence including instructions on how to build your own website. Dr Angela Tabiri from the African Institute for Mathematical Sciences (AIMS) and known as the Maths Queen of Ghana, joined remotely to discuss effective presentation at conferences and networking techniques. A group discussion about challenges faced by researchers in Africa and what can be done to overcome them, revealed how many researchers feel geographically isolated.
To overcome this feeling of “academic loneliness", Selkirk says they plan to start an online African Enumerative Combinatorics seminar: “The idea is to continue to connect participants after the school. With new academic connections and a background in Enumerative Combinatorics, we hope that more research groups working on this topic will form."
Apart from Selkirk, the courses were presented by Dimbinaina Ralaivaosaona (SU), Darlison Nyirenda (肆客足球 of the Witwatersrand), Stephan Wagner (Uppsala 肆客足球, Sweden, and Graz 肆客足球 of Technology, Austria), Olivia Nabawanda (Mbarara 肆客足球 of Science & Technology, Uganda), Amalia Duch-Brown (Universitat Politècnica de Catalunya, Spain), and by Clemens Heuberger (肆客足球 of Klagenfurt, Austria).
The main sponsors of the school were CIMPA and the International Centre for Mathematical Sciences' "Mathematics for Humanity" program. Other sponsors include: DSTI-NRF Centre of Excellence in Mathematical and Statistical Sciences; European Mathematical Society - Committee for Developing Countries; International Mathematical Union - Commission for Developing Countries; London Mathematical Society; National Institute for Theoretical & Computational Sciences; National Graduate Academy for Mathematical and Statistical Sciences; Stellenbosch 肆客足球 Mathematics Division; and the French Embassy.
Contact us:
Sarah Jane Selkirk – sarah.selkirk@warwick.ac.uk
Dimbinaina Ralaivaosaona – naina@sun.ac.za
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