Málstofa í stærðfræði
Fyrirlesari: Duncan Alexander Adamson, Háskólinn í Reykjavík
Titill: Combinatorial Structures for Crystal Structure Prediction
Staðsetning: Tg-227 í Tæknigarði.
Tímasetning: Fimmtudaginn 17. mars 2022, kl. 10:30.
Ágrip:
Crystals are a fundamental form of matter defined by a periodic structure with a high level of symmetry. The relatively small period of crystals allows the global properties of the structure to be predicted from a relatively small amount of information. Despite the advantages crystals have over other forms of matter, the problem of predicting the structure of a crystal has remained a major open problem spanning materials science, chemistry, and computer science.
In this talk we present a set of multidimensional necklaces, a multidimensional generalisation of combinatorial necklaces, designed to capture the symmetry within the translational space that is inherent to crystal structures. Along with the motivation and definition, we see how that several classical problems for one dimensional necklaces can be generalised to the multidimensional setting, including the problems of:
* Counting (determining the number of necklaces of a given size over a given alphabet)
* Generating (outputting every necklace of a given size over a given alphabet under some order)
* Ranking (determining the number of necklaces of a given size over a given alphabet that are smaller than some input necklace)
* Unranking (output the necklace with a given rank within the set of necklaces of some given size over a given alphabet)
Further, we provide efficient algorithms for solving each of these problems.