2024 Workshop on (Mostly) Matroids

On a q-analogue of perfect matroid designs

20 Aug 2024, 14:40

25m

S236 (IBS Science Culture Center)

Presentation (25 min)

Speaker

Shinya Kawabuchi (Kumamoto University)

Description

A Steiner system is characterized with the subsets (called blocks) satisfying that all $t$-subsets are included in exactly one block. A perfect matroid design (PMD) is a matroid whose flats of the same rank have the same size. Recently, E. Byrne et. al.  proposed a $q$-analogue of PMDs (namely $q$-PMDs) and constructed a non-trivial $q$-PMD from a $q$-analogue of a Steiner system. In this talk, we show some properties of $q$-PMDs and demonstrate that a certain class of $q$-PMDs induces a $q$-Steiner system.