Thesis supervisor: Eszter Katonáné Horváth
Location of studies (in Hungarian): SZTE Bolyai Intézet Abbreviation of location of studies: MatDI
Description of the research topic:
The aim is to find new mathematical results regarding enumerative problems related to finite algebraic structures. Series, sequences, knowledge from analysis might appear and apply.
If the algebraic structure obeys some regularity rules, e.g. coalition lattices, then the interesting and important structures - subuniverses, congruences, special elements - might be described by some recursive laws, and recursive laws might lead to nice numerical rules.
Not only the number of congruences, but also the number of some other kinds of preserved relations might be possible to determine.
3.The combinatorial results might lead to new structural properties and earlier structural results might lead to new numerical results. These areas provide several natural open problems.
Not only finite lattices, but also other kind of finite algebraic structures, e.g. groups, could be and should also be investigated from numerical point of view. For example, automorphism groups are important groups, and they are in connection with other properties of the algebra.
Which kind of algebraic structure can provide nice numerical result regarding some "classical properties"?
Mathematical importance: connection between enumerative mathematics (combinatorics) and algebra (mainly lattice-theory). The significance of Szeged in this topic is without question.
In digital world, numerical properties of finite structures can be of big interest.
Required language skills: English Number of students who can be accepted: 1
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