DisCoMath Seminar: Kristijan Tabak
Discrete & Computational Math Seminar (DisCoMath)
Surprising dualities of incidence structures across finite vector spaces
Kristijan Tabak
RIT Croatia
Abstract: A natural generalization of a symmetric design is usually made within the frame of a vector space over the finite field. With this in mind, we present new dualities in a ‘min-max’ way, meaning that some minimal substructures in a vector space (over finite field) are deeply related with the appropriate maximal structures in the same ambient space. Both ‘extremes’ are constructed using generalizations of a symmetric design and also, what it seems now, not related with classical concepts of residual or derived designs. This is still work in progress. We believe that this could yield to some new algebraic identities that may be interpreted as ‘Mobius like’ inversion formulas that we have seen in number theory.
Intended Audience: Undergraduates
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